List of SYNODE References on

Geometric Integration

The SYNODE Project is interested in references on the subject Geometric Integration, and would appreciate to be notified about new (or old) publications in this field. Please mail to Arne.Marthinsen@math.ntnu.no.
The list below is available as a BibTeX file.
  1. M. Ablowitz, B. M. Herbst, and C. Schober: On the numerics of integrable discretizations, In CRM Proceedings and Lecture Notes, Volume 6, pages 1-10. AMS, 1996.
  2. M. J. Ablowitz and S. Charkravarty: Integrability, computation and applications, Acta Applicandae Mathematicae, 39:5-37, 1995.
  3. M. J. Ablowitz, B. M. Herbst, and C. Schobert: On the numerical solution of the Sine-Gordon equation, I. Integrable discretizations and homoclinic manifolds, J. of Comp. Phys., 126:299-314, 1996.
  4. M. J. Ablowitz, B. M. Herbst, and C. Schobert: On the numerical solution of the Sine-Gordon equation, II. Performance of numerical schemes, J. of Comp. Phys., 131:354-367, 1997.
  5. R. Abraham and J. E. Marsden: Foundations of Mechanics, Addison-Wesley, Second edition, 1978.
  6. R. Abraham, J. E. Marsden, and T. Ratiu: Manifolds, Tensor Analysis, and Applications, AMS 75. Springer-Verlag, Second edition, 1988.
  7. L. Allen and T. J. Bridges: Numerical exterior algebra and the compound matrix method, 2001.
  8. V. I. Arnold: Mathematical Methods of Classical Mechanics, Springer-Verlag, GTM 60, Second edition, 1989.
  9. V. I. Arnold and B. A. Khesin: Topological Methods in Hydrodynamics, Number 125 in Applied Mathematical Sciences. Springer-Verlag, 1998.
  10. T. Arponen and J. Tuomela: On the numerical solution of involutive ordinary differential systems: Numerical results, Technical Report A370, Institute of Mathematics, Helsinki University of Technology, 1996.
  11. D. K. Arrowsmith and C. M. Place: Dynamical Systems: Differential Equations, Maps, and Chaotic Behavior, Chapman & Hall, New York, 1992.
  12. U. M. Ascher, H. Chin, and S. Reich: Stabilization of DAEs and invariant manifolds, Numer. Math., 67(2):131-149, 1994.
  13. U. M. Ascher and L. R. Petzold: Projected implicit Runge-Kutta methods for differential-algebraic equations, SIAM J. Numer. Anal., 28:1097-1120, 1991.
  14. U. M. Ascher and L. R. Petzold: Projected collocation methods for higher-order higher-index differential-algebraic equations, J. Comput. Appl. Math, 43:243-259, 1992.
  15. U. M. Ascher and L. R. Petzold: Stability of computational methods for constrained dynamics systems, SIAM J. Sci. Comput., 14:95-120, 1993.
  16. M. Austin, P. S. Krishnaprasad, and L.-S. Wang: Symplectic and almost poisson integration of rigid body systems, In S. Atluvi, editor, Proceedings of the 1991 International Conference on Computational Engineering Science, Melbourne, Australia, 1991.
  17. M. Austin, P. S. Krishnaprasad, and L.-S. Wang: Almost poisson integration of rigid body systems, J. of Comp. Phys., 107:105-117, 1993.
  18. J. L. R. Azara: A MAPLE program for the generation of the Lie-series solution of systems of non-linear ordinary differential equations, Comput. Phys. Comm., 67:537-542, 1992.
  19. H. F. Baker: Alternants and continuous groups, Proc. London Math. Soc., 3:24-47, 1905.
  20. M. I. Bakirova, V. A. Dorodnitsyn, and R. V. Kozlov: Symmetry preserving discrete schemes for some heat transfer equations, J. Phys. A: Math. Gen., 1997.
  21. M. Barr and C. Wells: Category Theory for Computing Science, Prentice Hall, 1990.
  22. E. Barth and B. J. Leimkuhler: Symplectic methods for conservative multibody systems, Fields Inst. Com., 1995.To appear.
  23. S. Blanes, F. Casas, and J. Ros: Improved high order integrators based on the Magnus expansion, BIT, 40(3):434-450, 2000.
  24. S. Blanes, F. Casas, and J. Ros: High order optimized geometric integrators for linear differential equations, BIT, 42(2):262-284, 2002.
  25. S. Blanes and P. C. Moan: Splitting methods for non-autonomous differential equations, Technical Report 1999/NA21, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1999.
  26. A. M. Bloch, R. W. Brockett, and P. E. Crouch: Double bracket equations and geodesic flows on symmetric spaces, Comm. Math. Phys., 187(2):357-373, 1997.
  27. A. M. Bloch and P. E. Crouch: Optimal control and geodesic flows, Systems Control Lett., 28(2):65-72, 1996.
  28. W. M. Boothby: An Introduction to Riemannian Geometry, Academic Press, 1975.
  29. C. A. Botsaris: Constrained optimization along geodesics, J. of Math. Anal. and Applic., 79:295-306, 1981.
  30. C. L. Bottasso and M. Borri: Integrating finite rotations, Preprint submitted to Comp. Methods Appl. Mech. Engrg., 1997.
  31. N. Bourbaki: Lie groups and Lie algebras, Part I, Chapters 1-3, Addison-Wesley, 1975.
  32. P. Brenner, V. Mehrmann, and H. Xu: A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils, Numer. Math., 78(3):329-358, 1998.
  33. R. Brockett: Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems, Lin. Alg. Applic., 146:79-91, 1991.
  34. R. Brockett: The double bracket equation as the solution of a variational problem, Fields Inst. Com., 3:69-76, 1994.
  35. R. L. Bryant: An introduction to Lie groups and symplectic geometry, In D. S. Freed and K. K. Uhlenbeck, editors, Geometry and Quantum Field Theory, volume 1, Second Edition of IAS/Park City Mathematics Series. American Mathematical Society, 1995.
  36. C. J. Budd, G. J. Collins, W. Z. Huang, and R. D. Russell: Self-similar numerical solutions of the porous-medium equation using moving mesh methods, Phil. Trans. Royal Soc. A, 357:1047-1078, 1999.
  37. C. J. Budd and A. Iserles: Geometric integration: Numerical solution of differential equations on manifolds, In C. J. Budd and A. Iserles, editors, Geometric Integration: Numerical Solution of Differential Equations on Manifolds, volume 357 of Philosophical Transactions of the Royal Society A, pages 945-956. London Mathematical Society, 1999.
  38. C. J. Budd and M. D. Piggott: Geometric integration and its applications, 2001, To appear in Foundations of Computational Mathematics, a volume of the Handbook of Numerical Analysis, ed. Ph. G. Chiarlet and F. Cucker, published by Elsevier Science.
  39. M. P. Calvo, A. Iserles, and A. Zanna: Runge-Kutta methods on manifolds, In D. F. Griffiths and G. A. Watson, editors, A. R. Mitchell's 75th Birthday Volume, pages 57-70. World Scientific, Singapore, 1996.
  40. M. P. Calvo, A. Iserles, and A. Zanna: Runge-Kutta methods for orthogonal and isospectral flows, Appl. Numer. Math., 22:153-163, 1996.
  41. M. P. Calvo, A. Iserles, and A. Zanna: Numerical solution of isospectral flows, Math. Comp., 66(220):1461-1486, 1997.
  42. M. P. Calvo, A. Iserles, and A. Zanna: Semi-explicit methods for isospectral flows, Technical Report 1997/NA16, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1997.To appear in Adv. Comp. Math.
  43. M. P. Calvo, A. Iserles, and A. Zanna: Conservative methods for the Toda lattice equations, IMA J. Numer. Anal., 19(4):509-523, 1999.
  44. M. P. Calvo, M. A. López-Marcos, and J. M. Sanz-Serna: Variable step implementation of geometric integrators, Appl. Numer. Math., 28(1):1-16, 1998.
  45. J. E. Campbell: On a law of combination of operators bearing on the theory of continuous transformation groups, Proc. London Math. Soc., 28:381-390, 1897.
  46. B. Cano and J. M. Sanz-Serna: Error growth in the numerical integration of periodic orbits, with application to Hamiltonian and reversible systems, SIAM J. Numer. Anal., 34(4):1391-1417, 1997.
  47. B. Cano and J. M. Sanz-Serna: Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems, IMA J. Numer. Anal., 18(1):57-75, 1998.
  48. R. Carter, G. Segal, and I. MacDonald: Lectures on Lie Groups and Lie Algebras, volume 32 of Student Texts, London Mathematical Society, 1995.
  49. F. Casas: Fer's factorization as a symplectic integrator, Numer. Math., 74(3):283-303, 1996.
  50. F. Casas: Solution of linear partial differential equations by Lie algebraic methods, J. Comput. Appl. Math, 76:159-170, 1996.
  51. F. Casas, J. A. Oteo, and J. Ros: Lie algebraic approach to Fer's expansion for classical Hamiltonian systems, J. Phys. A: Math. Gen., 24:4037-4046, 1991.
  52. E. Celledoni: A note on the numerical integration of the KdV equation via isospectral deformations, J. Phys. A: Math. Gen., 34(11):2205-2214, 2001.
  53. E. Celledoni and A. Iserles: Approximating the exponential from a Lie algebra to a Lie group, Math. Comp., 2000.Posted on March 15, PII S 0025-5718(00)01223-0 (to appear in print).
  54. E. Celledoni and A. Iserles: Methods for the approximation of the matrix exponential in a Lie-algebraic setting, 21(2):463-488, 2001.
  55. E. Celledoni, A. Iserles, S. P. Nørsett, and B. Orel: Complexity theory for Lie-group solvers, Technical Report 1999/NA20, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1999.
  56. E. Celledoni, A. Iserles, S. P. Nørsett, and B. Orel: Complexity theory for Lie-group solvers, J. of Complexity, 18(1), 2002.
  57. E. Celledoni and B. Owren: Lie group methods for rigid body dynamics and time integration on manifolds, Technical report, The Norwegian University of Science and Technology, Trondheim, Norway, 1999.
  58. E. Celledoni and B. Owren: A class of low complexity intrinsic schemes for orthogonal integration, Technical Report Numerics No. 1/2001, The Norwegian University of Science and Technology, Trondheim, Norway, 2001.
  59. E. Celledoni and B. Owren: On the implementation of Lie group methods on the Stiefel manifold, Technical Report Numerics No. 9/2001, The Norwegian University of Science and Technology, Trondheim, Norway, 2001.
  60. P. Channell: Symplectic integration for particles in electric and magnetic fields, Accelerator Theory Note, No. AT-6: ATN-86-5, Los Alamos National Laboratory, 1986.
  61. A. Chorin, T. J. R. Huges, J. E. Marsden, and M. McCracken: Product formulas and numerical algorithms, Comm. Pure and Appl. Math., 31:205-256, 1978.
  62. G. J. Cooper: Stability of Runge-Kutta methods for trajectory problems, IMA J. Numer. Anal., 7:1-13, 1987.
  63. P. E. Crouch: Spacecraft altitude control and stabilization: Application of geometric control to rigid body models, IEEE Trans. Automatic Control, AC-29:321-331, 1986.
  64. P. E. Crouch and R. Grossman: Numerical integration of ordinary differential equations on manifolds, J. Nonlinear Sci., 3:1-33, 1993.
  65. P. E. Crouch, R. Grossman, and R. L. Larson: Trees, bialgebras, and intrinsic numerical integrators, Technical Report #LAC90-R23, Laboratory for Advanced Computing, University of Illinois at Chicago, 1990.
  66. P. E. Crouch, R. Grossman, and R. L. Larson: Computations involving differential operators and their actions on functions, In Proceedings of the 1991 International Symposium of Algebraic and Symbolic Computation. ACM, 1991.
  67. P. E. Crouch, R. Grossman, and Y. Yan: A third order geometrically stable Runge-Kutta algorithm on a manifold, 1992.
  68. P. E. Crouch, G. Kun, and F. Silva Leite: The De Casteljau algorithm on Lie groups and spheres, To appear.
  69. P. E. Crouch, G. Kun, and F. Silva Leite: Generalization of spline curves on the sphere: A numerical comparison, To appear.
  70. P. E. Crouch, G. Kun, and F. Silva Leite: De Casteljau algorithm for cubic polynomials on the rotation group, In Proc. CONTROLO-96, Vol. II, 547-552, 1996.
  71. P. E. Crouch and R. L. Larson: The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomial coefficients using trees, In Proceedings of the 1992 International Symposium of Algebraic and Symbolic Computation. ACM, 1992.
  72. P. E. Crouch and F. Silva Leite: The dynamic interpolation problem: On Riemannian manifolds, Lie groups, and symmetric spaces, J. Dynamical and Control Systems, 1(2):177-202, 1995.
  73. P. E. Crouch, Y. Yan, and R. Grossman: On the numerical integration of the dynamic attitude equations.
  74. P. E. Crouch, Y. Yan, and R. Grossman: On the numerical integration of the rolling ball equations using geometrically exact algorithms, J. Mech. Struct. and Mach., 23:257-272, 1995.
  75. M. L. Curtis: Matrix Groups, Springer-Verlag, Second edition, 1984.
  76. R. de Vogelaere: Methods of integration which preserve the contact transformation property of the Hamiltonian equations, Technical Report 4, Department of Mathematics, University of Notre Dame.
  77. N. del Buono and L. Lopez: Runge-Kutta type methods based on geodesics for systems of ODEs on the Stiefel manifold, BIT, 41(5):912-923, 2001.
  78. L. Dieci and T. Eirola: Preserving monotonicity in the numerical solution of Riccati differential equations, Numer. Math., 74:35-47, 1996.
  79. L. Dieci, R. D. Russell, and E. S. van Vleck: Unitary integrators and applications to continuous orthonormalization techniques, SIAM J. Numer. Anal., 31, No. 1:261-281, 1994.
  80. L. Dieci and E. S. Van Vleck: Computation of orthonormal factors for fundamental solution matrices, Numer. Math., 83:599-620, 1999.
  81. F. Diele, L. Lopez, and R. Peluso: The Cayley transform in the numerical solution of unitary differential systems, Adv. Comput. Math., 8(4):317-334, 1998.
  82. F. Diele, L. Lopez, and T. Politi: One step semi-explicit methods based on the Cayley transform for solving isospectral flows, J. Comput. Appl. Math, 89:219-223, 1998.
  83. V. Dorodnitsyn: Finite difference methods entirely inheriting the symmetry of the original equations, In N. Ibragimov, editor, Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, pages 191-201. Kluwer, 1993.
  84. V. Dorodnitsyn and R. Kozlov: Second-order ordinary difference equations admitting Lie-point transformations, Technical Report Numerics No. 3/1998, The Norwegian University of Science and Technology, Trondheim, Norway, 1998.
  85. V. Dorodnitsyn and R. Kozlov: A heat transfer with a source: the complete set of invariant difference schemes, 10(1):16-50, 2003.
  86. V. Dorodnitsyn, R. Kozlov, and P. Winternitz: Lie group classification of second-order ordinary difference equations, J. of Math. Phys., 41(1):480-504, 2000.
  87. V. Dorodnitsyn, R. Kozlov, and P. Winternitz: Second order ordinary difference equations with symmetries: Lagrangian formalism, first integrals and exact solutions, 2000.
  88. A. J. Dragt: Lie methods for nonlinear dynamics with applications to accelerator physics, Technical report, University of Maryland Physics Department, 1999.
  89. A. J. Dragt and J. M. Finn: Lie series and invariant functions for analytic symplectic maps, J. of Math. Phys., 17:2215-2227, 1976.
  90. A. Edelman, T. Arias, and S. T. Smith: Conjugate gradient on the Stiefel and Grassmann manifolds.
  91. A. Edelman, T. Arias, and S. T. Smith: Conjugate gradient and Newton's method on the Grassmann and Stiefel manifolds, 1996, Submitted to SIAM J. Matrix Anal. Appl.
  92. A. Edelman, T. A. Arias, and S. T. Smith: The geometry of algorithms with orthogonality constraints, SIAM J. Matrix Anal. Applic., 20(2):303-353, 1999.
  93. E. Eich, C. Führer, B. J. Leimkuhler, and S. Reich: Stabilization and projection methods for multibody dynamics, 1991.
  94. N. A. Elnatanov and J. Schiff: The Hamilton-Jacobi difference equation, To appear.
  95. K. Engø: On the BCH-formula in so(3), Technical Report No. 201, Department of Informatics, University of Bergen, Norway, 2000.
  96. K. Engø: On the construction of geometric integrators in the RKMK class, BIT, 40(1):41-61, 2000.
  97. K. Engø: Partitioned Runge-Kutta methods in Lie-group setting, Technical Report No. 202, Department of Informatics, University of Bergen, 2000.
  98. K. Engø and S. Faltinsen: Numerical integration of Lie-Poisson systems while preserving coadjoint orbits and energy, SIAM J. Numer. Anal., 39(1):128-145, 2001.
  99. K. Engø and A. Marthinsen: A note on the numerical solution of the heavy top equations, To appear in Multibody System Dynamics.
  100. K. Engø and A. Marthinsen: Application of geometric integration to some mechanical problems, Technical Report No. 132, Department of Informatics, University of Bergen, April 1997.
  101. K. Engø and A. Marthinsen: Modeling and solution of some mechanical problems on Lie groups, Multibody System Dynamics, 2:71-88, 1998.
  102. K. Engø and A. Marthinsen: Time-symmetry of Crouch-Grossman methods, Technical Report Numerics No. 2/2000, The Norwegian University of Science and Technology, Trondheim, Norway, 2000.
  103. K. Engø and A. Marthinsen: A note on the numerical solution of the heavy top equations, Multibody System Dynamics, 5(4):387-397, 2001.
  104. K. Engø, A. Marthinsen, and H. Z. Munthe-Kaas: DiffMan - an object oriented MATLAB toolbox for solving differential equations on manifolds, Technical Report No. 164, Department of Informatics, University of Bergen, 1999.
  105. K. Engø, A. Marthinsen, and H. Z. Munthe-Kaas: Diffman user's guide, version 1.6, Technical Report No. 166, Department of Informatics, University of Bergen, 1999.
  106. T. Ergenç and B. Karasözen: Runge-Kutta collocation methods for rigid body Lie-Poisson equations, Internat. J. Comput. Math., 62:63-71, 1996.
  107. S. Faltinsen: Backward error analysis for Lie-group methods, BIT, 40(4):652-671, 2000.
  108. S. Faltinsen, A. Marthinsen, and H. Z. Munthe-Kaas: Multistep methods integrating ordinary differential equations on manifolds, Technical Report Numerics No. 3/1999, The Norwegian University of Science and Technology, Trondheim, Norway, 1999.
  109. K. Feng and Z.-J. Shang: Volume-preserving algorithms for source-free dynamical systems, Numer. Math., 71:451-463, 1995.
  110. F. Fer: Résolution del l`equation matricielle dotU=pU par produit infini d`exponentielles matricielles, Bull. Classe des Sci. Acad. Royal Belg., 44:818-829, 1958.
  111. E. Forest: Sixth-order Lie group integrators, J. of Comp. Phys., 99:209-213, 1992.
  112. D. D. Fox and J. C. Simo: A drill rotation formulation for geometrically exact shells, Comput. Methods Appl. Mech. Engrg., 98:329-343, 1992.
  113. C. Führer and B. J. Leimkuhler: Formulation and numerical solution of the equations of constrained mechanical motion, Technical Report DFVLR-FB 89-08, Institut für Dynamik der Flugsysteme, Oberpaffenhofen, Germany, 1989.
  114. W. Fulton and J. Harris: Representation Theory - A First Course, Springer-Verlag, 1991.
  115. B. Garcia-Archilla, J. M. Sanz-Serna, and R. D. Skeel: Long-time-steps methods for oscillatory differential equations, SIAM J. Sci. Comput., 20(3):930-963, 1999.
  116. Ge-Zhong and J. Marsden: Lie-Poisson Hamiltonian-Jacobi theory and Lie-Poisson integrators, Phys. Lett., 133:134-139, 1988.
  117. E. N. Gilbert and J. Riordan: Symmetry types of periodic sequences, Illinois J. Math., 5:657-665, 1961.
  118. O. Gonzalez: Mechanical systems subject to holonomic constraints: Differential-algebraic formulations and conservative integration, Technical report, Division of Applied Mathematics, Department of Mechanical Engineering, Stanford University, 1996.
  119. O. Gonzalez: Time integration and discrete Hamiltonian systems, J. Nonlinear Sci., 6:449-467, 1996.
  120. O. Gonzalez and J. C. Simo: On the stability of symplectic and energy-momentum algorithms for nonlinear hamiltonian systems with symmetry, Comput. Methods Appl. Mech. Engrg., 134:197-222.
  121. O. Gonzalez and J. C. Simo: On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry, Technical report, Div. of Appl. Mech., Dept. of Mech. Eng., Stanford Univ., USA, 1994.
  122. R. Grossman: Evaluation of expressions involving higher order derivations, J. of Math. Systems, Estimation, and Control, 1, No. 1:91-106, 1991.
  123. R. Grossman and P. E. Crouch: The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomial coefficients using trees, 1992.
  124. R. Grossman and R. G. Larson: Solving nonlinear equations from higher order derivations in linear stages, Advances in Mathematics, 82, No. 2:180-202, 1990.
  125. R. Grossman and R. G. Larson: Symbolic computation of derivations using labelled trees, Journal of Symbolic Computation, 13:511-523, 1992.
  126. V. Guillemin and A. Pollack: Differential Topology, Prentice-Hall, Englewood Cliffs, 1974.
  127. H. Gümral and Y. Nutku: Poisson structure of dynamical systems with three degrees of freedom, J. of Math. Phys., 34:5691-5723, 1993.
  128. F. A. Haggar, G. B. Byrnes, G. R. W. Quispel, and H. W. Capel: k-integrals and k-Lie symmetries in discrete dynamical systems, To appear.
  129. E. Hairer: Symmetric projection methods for differential equations on manifolds, BIT, 40(4):726-734, 2000.
  130. E. Hairer: Geometric integration of ordinary differential equations on manifolds, BIT, 41(5):996-1007, 2001.
  131. E. Hairer, C. Lubich, and M. Roche: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Springer-Verlag, 1989.
  132. E. Hairer and Ch. Lubich: The life-span of backward error analysis for numerical integrators, Numer. Math., 76:441-462, 1997.
  133. E. Hairer, Ch. Lubich, and G. Wanner: Geometric Numerical Integration, Number 31 in Springer Series in Computational Mathematics. Springer-Verlag, 2002.
  134. E. Hairer, S. P. Nørsett, and G. Wanner: Solving Ordinary Differential Equations I, Nonstiff Problems, Springer-Verlag, Second revised edition, 1993.
  135. F. Hausdorff: Die symbolische Exponential Formel in der Gruppen theorie, Leipziger Ber., 58:19-48, 1906.
  136. S. Helgason: Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, 1978.
  137. D. J. Higham: Runge-Kutta type methods for orthogonal integration, In J. C. Butcher, editor, Applied Numerical Mathematics (special issue celebrating the Runge-Kutta centenary), volume 22, pages 217-223, 1996.
  138. D. J. Higham: Runge-Kutta type methods for orthogonal integration, Technical Report NA/168, Department of Mathematics and Computer Science, University of Dundee, 1996.
  139. D. J. Higham: Time-stepping and preserving orthonormality, BIT, 37(1):24-36, 1997.
  140. L. Hlavaty, S. Steinberg, and B. Wolf: Riccati equations and Lie series, J. of Math. Anal. and Appl., 104:246-263, 1984.
  141. M. Hochbruck and C. Lubich: A bunch of time integrators for quantum/classical molecular dynamics, Technical report, Mathematisches Institut, Universit"at Tübingen, 1997.
  142. M. Hochbruck, C. Lubich, and H. Selhofer: Exponential integrators for large systems of differential equations, SIAM J. Sci. Comput., 19(5):1552-1574, 1998.
  143. M. Hochbruck and Ch. Lubich: On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 34(5), 1997.
  144. J. E. Humphreys: Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics. Springer-Verlag, 1972.
  145. A. Iserles: Solving linear ordinary differential equations by exponentials of iterated commutators, Numer. Math., 45:183-199, 1984.
  146. A. Iserles: Beyond the classical theory of computational ordinary differential equations, In I.S. Duff and G.A. Watson, editors, State of the Art in Numerical Analysis, pages 171-192. Oxford University Press, Oxford, 1997.
  147. A. Iserles: Multistep methods on manifolds, Technical Report 1997/NA13, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1997.
  148. A. Iserles: Numerical methods on (and off) manifolds, In F. Cucker and M. Shub, editors, Foundation of Computational Mathematics, pages 180-189. Springer-Verlag, 1997.
  149. A. Iserles: How large is the exponential of a banded matrix?, Technical Report 1999/NA01, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1999.
  150. A. Iserles: On Cayley-transform methods for the discretization of Lie-group equations, Technical Report 1999/NA4, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1999.
  151. A. Iserles: Brief introduction to Lie-group methods, To appear in proceedings of the Fort Collins workshop on preservation of stability under discretization (Don Estep & Simon Tavener, eds.), to be published by SIAM, 2001.
  152. A. Iserles: Lie groups and the computation of invariants, Hermis, 2:53-68, 2001.
  153. A. Iserles: On Cayley-transform methods for the discretization of Lie-group equations, Foundations of Computational Mathematics, 1(1):129-160, 2001.
  154. A. Iserles: On the discretization of double-bracket flows, 2001.
  155. A. Iserles: Think globally, act locally: Solving highly-oscillatory ordinary differential equations, 2001, Submitted to the special issue of Applied Numerical Mathematics devoted to the 2001 Dundee conference.
  156. A. Iserles: On the global error of discretization methods for highly-oscillatory ordinary differential equations, BIT, 42(3):561-599, 2002.
  157. A. Iserles, A. Marthinsen, and S. P. Nørsett: On the implementation of the method of Magnus series for linear differential equations, BIT, 39(2):281-304, 1999.
  158. A. Iserles, R. I. McLachlan, and A. Zanna: Approximately preserving symmetries in numerical integration, Technical Report 1997/NA22, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1997.To appear in Euro. J. Appl. Math.
  159. A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, and A. Zanna: Lie-group methods, Acta Numerica, 9:215-365, 2000.
  160. A. Iserles and S. P. Nørsett: Linear ODEs in Lie groups, In A. Sydow, editor, Proceedings of the 15th IMACS World Congress, volume II, pages 589-594. Wissenschaft & Technik Verlag, Berlin, 1997.
  161. A. Iserles and S. P. Nørsett: On the solution of linear differential equations in Lie groups, Phil. Trans. Royal Soc. A, 357:983-1020, 1999.
  162. A. Iserles, S. P. Nørsett, and A. F. Rasmussen: Reversibility and high-order Magnus methods, Technical Report 1998/NA06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1998.
  163. A. Iserles and A. Zanna: Qualitative numerical analysis of ordinary differential equations, In J. Renegar, M. Shub, and S. Smale, editors, Lectures in Applied Mathematics. AMS, Providence RI, 1995.DAMTP Technical Report 1995/NA05.
  164. A. Iserles and A. Zanna: A scalpel, not a sledgehammer: Qualitative approach to numerical mathematics, CWI Quarterly, 9:103-112, 1996.
  165. A. Iserles and A. Zanna: On the dimension of certain graded Lie algebras arising in geometric integration of differential equations, Technical Report 1999/NA06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1999.
  166. A. Iserles and A. Zanna: Preserving algebraic invariants with Runge-Kutta methods, Technical Report 1999/NA12, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1999.
  167. Z. Jackiewicz, A. Marthinsen, and B. Owren: Construction of Runge-Kutta methods of Crouch-Grossman type of high order, Adv. Comput. Math., 13(4):405-415, 2000.
  168. G. Jacob and P.-V. Koseleff (Eds.): Special issue on Lie computations, Discrete Mathematics and Theoretical Computer Science, 1(1):99-266, 1997.Electronic journal: http://dmtcs.thomsonscience.com/.
  169. N. Jacobson: Lie Algebras, Dover Publications, Inc., New York, 1979.
  170. L. O. Jay: Structure preservation for constrained dynamics with super partitioned additive Runge-Kutta methods, SIAM J. Sci. Comput., 20(2):416-446, 1999.
  171. D. A. Jones and A. M. Stuart: Attractive invariant manifolds under approximation. Inertial manifolds, J. Differential Equations, 123(2):588-637, 1995.
  172. F. Kang and S. Zai-jiu: Volume-preserving algorithmms for source-free dynamical systems, Numer. Math., 71(4):451-463, 1995.
  173. S. Kang and M. Kim: Free Lie algebras, generalized Witt formula, and the denominator identity, J. Algebra, 183:560-594, 1996.
  174. B. Karasözen: Reflexive methods for dynamical systems with conserved quantities, Technical Report Mathematics 96/128, Faculty of Arts and Sciences, Middle East Technical University, Ankara, Turkey, 1996.Also available as Technical Report Nr. 1897, Technische Hochschule Darmstadt, 1997.
  175. B. Karasözen and A. Pamir: Structure-preserving splitting methods for lotka-volterra equations, Technical Report Mathematics 165/98, Faculty of Arts and Sciences, Middle East Technical University, Ankara, Turkey, 1998.
  176. W. Klingenberg: Riemannian Geometry, Walter de Gruyter, New York, 1982.
  177. S. Kobayashi and K. Nomizu: Foundations of Differential Geometry, volume I, Wiley, 1996.
  178. M. Kolsrud: Maximal reductions in the Baker-Hausdorff formula, J. of Math. Phys., 34(1):270-285, 1993.
  179. B. Komrakov, A. Churyumov, and B. Doubrov: Two-dimensional homogeneous spaces, Technical Report Preprint Series No. 17, Institute of Mathematics, University of Oslo, Norway, 1993.
  180. B. Komrakov and V. Lychagin: Symmetries and integrals, Technical Report Preprint Series No. 15, Institute of Mathematics, University of Oslo, Norway, 1993.
  181. B. Koobus and C. Farhat: Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes, Technical Report CU-CAS-97-12, Center for Aerospace Structures, College of Engineering, University of Colorado, Campus Box 429, Boulder, Colorado 80309, 1997.
  182. P.-V. Koseleff: Calcul formel pour les méthodes de Lie en mécanique, PhD thesis, Ecole Polytechnique, 1993.
  183. P. V. Koseleff: Relations among formal Lie series and construction of symplectic integrators, In G. Cohen, T. Mora, and O. Moreno, editors, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, pages 212-230. Springer-Verlag, 1993.
  184. P.-V. Koseleff: About approximations of exponentials, In Proceedings of AAECC'11 Conference, Paris, volume 948 of LNCS, pages 323-333, 1997.
  185. P.-V. Koseleff: Relations among Lie series transformations and isomorphisms between free Lie algebras, Discrete Methematics, 180(1-3):243-254, 1998.
  186. R. Kozlov: Conservation laws of semidiscrete canonical Hamiltonian equations, J. Phys. A: Math. Gen., 34(17):3651-3669, 2001.
  187. R. Kozlov: Conservation laws of semidiscrete Hamiltonian equations, J. of Math. Phys., 42(4):1708-1727, 2001.
  188. A. J. Krener and R. Hermann: Nonlinear observability and controllability, IEEE Trans. Automatic Control, AC-22:728-740, 1977.
  189. S. Krogstad: A low complexity Lie group method on the Stiefel manifold, 2001.
  190. A. Kvaernø and B. J. Leimkuhler: Time reversible N-body integrators based on smooth switches, SIAM J. Sci. Comput., 22(3):1016-1035, 2000.
  191. R. A. LaBudde and D. Greenspan: Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion. Part I, Numer. Math., 25:323-346, 1976.
  192. R. A. LaBudde and D. Greenspan: Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion. Part II, Numer. Math., 26:1-16, 1976.
  193. S. Lang: Differential and Riemannian Manifolds, Springer-Verlag, 1995.
  194. A. M. Latypov: Approximate Lie group analysis of a model advection equation on an unstructured grid, Technical report, Department of Mathematics and Statistics and Fluid Dynamics Research Institute, University of Windsor, 401 Sunset Ave., Windsor, Ontario, Canada N9B 3P4, 1995.
  195. A. M. Latypov: Approximate Lie group analysis of finite-difference equations, Technical report, Department of Mathematics and Statistics and Fluid Dynamics Research Institute, University of Windsor, 401 Sunset Ave., Windsor, Ontario, Canada N9B 3P4, 1995.
  196. B. J. Leimkuhler: Reversible adaptive regularization: Perturbed Kepler motion and classical atomic trajectories, Phil. Trans. Royal Soc. A, 357:1101, 1999.
  197. B. J. Leimkuhler and G. W. Patrick: A symplectic integrator for Riemannian manifolds, J. Nonlinear Sci., 6(4):367-384, 1996.
  198. B. J. Leimkuhler and S. Reich: Symplectic integraton of constrained Hamiltonian systems, Math. Comp., 65:589-605, 1994.
  199. B. J. Leimkuhler and E. S. van Vleck: Orthosymplectic integration of linear Hamiltonian systems, Numer. Math., 77:269-282, 1997.
  200. N. E. Leonard and J. E. Marsden: Stability and drift of uniderwater vehicle dynamics: Mechanical systems with rigid motion symmetry, Physica D, 105(1-3):130-162, 1997.
  201. M. Lesoinne and C. Farhat: Geometric conservation laws for aeroelastic computations using unstructured dynamics meshes, Technical Report AIAA-95-1709, American Institute of Aeronautics and Astronautics, 1995.
  202. D. Lewis and P. J. Olver: Geometric integration algorithms on homogeneous manifolds, Foundations of Computational Mathematics, 2(4):363-392, 2002.
  203. D. Lewis, T. Ratiu, J. C. Simo, and J. E. Marsden: The heavy top: A geometric treatment, Nonlinearity, 5(1):1-48, 1992.
  204. D. Lewis and J. C. Simo: Nonlinear stability of rotating pseudo-rigid bodies, Proc. R. Soc. Lond. A, 427(1873):281-319, 1990.
  205. D. Lewis and J. C. Simo: Conserving algorithms for the dynamics of Hamiltonian systems of Lie groups, J. Nonlinear Sci., 4:253-299, 1994.
  206. D. Lewis and J. C. Simo: Conserving algorithms for the n dimensional rigid body, Fields Inst. Com., 10, 1995.
  207. R.-C. Li: Raising the Orders of Unconventional Schemes for Ordinary Differential Equations, PhD thesis, University of California at Berkeley, 1995.
  208. S. T. Li and M. Qin: Lie-Poisson integration for rigid body dynamics, Computers Math. Applic., 30:105-118, 1995.
  209. S. T. Li and M. Qin: A note for Lie-Poisson Hamilton-Jacobi equation and Lie-Poisson integrator, Computers Math. Applic., 30:67-74, 1995.
  210. S. Lie and F. Engel: Theorie der Transformationsgruppen, B. G. Teubner, Leipzig, 1888, 1890, 1893.
  211. L. Lopez and T. Politi: Numerical procedures based on Runge-Kutta methods for solving isospectral flows, Appl. Numer. Math., 25:443-459, 1997.
  212. Ch. Lubich: Integration of stiff mechanical systems by Runge-Kutta methods, Z. Angew. Math. Phys., 44:1022-1053, 1993.
  213. A. J. Maciejewski and J. M. Strelcyn: The observer-new method for numerical integration of differential equations in the presence of first integrals, In A. E. Roy and B. A. Steves, editors, From Newton to Chaos, pages 503-512. Plenum, 1995.
  214. W. Magnus: On the exponential solution of differential equations for a linear operator, Comm. Pure and Appl. Math., VII:649-673, 1954.
  215. W. Magnus and S. Winkler: Hill's Equation, Interscience publishers, 1966.
  216. R. E. Mahony: The constrained Newton method on a Lie-group and the symmetric eigenvalue problem, Lin. Alg. Applic., 248:67-90, 1996.
  217. J. E. Marsden: Lectures on Mechanics, volume 174 of London Mathematical Society Lecture Note Series, Cambridge University Press, 1992.
  218. J. E. Marsden: Some remarks on geometric mechanics, Duration and Change, 254-274, 1994.Springer, Berlin.
  219. J. E. Marsden: Remarks on geometric mechanics, Preprint, 1996.
  220. J. E. Marsden, G. W. Patrick, and S. Shkoller: Multisymplectic geometry, variational integrators, and nonlinear PDEs, To appear in Comm. Math. Phys.
  221. J. E. Marsden and T. S. Ratiu: Introduction to Mechanics and Symmetry, Springer-Verlag, 1994.
  222. J. E. Marsden and T. S. Ratiu: Introduction to Mechanics and Symmetry, Number 17 in Texts in Applied Mathematics. Springer-Verlag, second edition, 1999.
  223. J. E. Marsden and M. West: Discrete mechanics and variational integrators, Acta Numerica, 10:357-514, 2001.
  224. A. Marthinsen: Interpolation in Lie groups, SIAM J. Numer. Anal., 37(1):269-285, 1999.
  225. A. Marthinsen: Numerical Integration of Ordinary Differential Equations on Manifolds via Lie Group Actions, PhD thesis, Norwegian University of Science and Technology, Trondheim, Norway, 1999.
  226. A. Marthinsen, H. Munthe-Kaas, and B. Owren: Simulation of ordinary differential equations on manifolds - some numerical experiments and verifications, Modeling, Identification and Control, 18:75-88, 1997.
  227. A. Marthinsen and B. Owren: Quadrature methods based on the Cayley transform, Technical Report Numerics No. 1/1999, The Norwegian University of Science and Technology, Trondheim, Norway, 1999.
  228. A. Marthinsen and B. Owren: A note on the construction of Crouch-Grossman methods, BIT, 41(1):207-214, 2001.
  229. R. I. McLachlan: Spatial discretization of partial differential equations with integrals, Submitted to SIAM J. Numer. Anal.
  230. R. I. McLachlan: Explicit Lie-Poisson integration and the Euler equations, Physical Review Letters, 71:3043-3046, 1993.
  231. R. I. McLachlan: Explicit symplectic splitting methods applied to PDE's, In E. L. Allwoger, K. Georg, and R. Miranda, editors, Lectures in Applied Mathematics: Exploiting Symmetry in Applied and Numerical Analysis, pages 325-337. American Mathematical Society, 1993.
  232. R. I. McLachlan: Comment on "Poisson schemes for Hamiltonian systems on Poisson manifolds", Computers Math. Applic., 29:1, 1995.
  233. R. I. McLachlan: Composition methods in the presence of small parameters, BIT, 35:258-268, 1995.
  234. R. I. McLachlan: On the numerical integration of ODE's by symmetric composition methods, SIAM J. Numer. Anal., 16:151-168, 1995.
  235. R. I. McLachlan: Families of high-order composition methods, 2001.
  236. R. I. McLachlan and G. R. W. Quispel: Generating functions for dynamical systems with symmetries, integrals, and differential invariants, Physica D, 112:298-309, 1997.
  237. R. I. McLachlan and G. R. W. Quispel: What kind of dynamics are there? Lie pseudogroups, dynamical systems, and geometric integration, 2001.
  238. R. I. McLachlan, G. R. W. Quispel, and N. Robidoux: A unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions and/or first integrals, Physical Review Letters, 81:2399-2403, 1998.
  239. R. I. McLachlan, G. R. W. Quispel, and N. Robidoux: Geometric integration using discrete gradients, Phil. Trans. Royal Soc. A, 357:1021-1046, 1999.
  240. R. I. McLachlan, G. R. W. Quispel, and G. S. Turner: Numerical integrators that preserve symmetries and reversing symmetries, SIAM J. Numer. Anal., 35(2):586-599, 1998.
  241. R. I. McLachlan and C. Scovel: Equivariant constrained symplectic integration, J. Nonlinear Sci., 16:233-256, 1995.
  242. R. I. McLachland and Matthew Perlmutter: Energy drift in reversible time integration, 2001, Submitted to Physics Letters A.
  243. G. Meyer: On the use of Euler's theorem on rotations for the synthesis of attitude control systems, Technical report, NASA Technical Note, NASA TN.D-3643, Ames Research Center, Moffet Field, California, 1966.
  244. P. C. Moan: The numerical solution of ordinary differential equations with conservation laws, Master's thesis, The Norwegian University of Science and Technology, 1996.
  245. P. C. Moan: Efficient approximation of Sturm-Liouville problems using Lie-group methods, Technical Report 1998/NA11, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1998.
  246. P. C. Moan, J. A. Oteo, and J. Ros: On the existence of the exponential solution of linear differential systems, J. Phys. A: Math. Gen., 32:5133-5139, 1999.
  247. J. B. Moore, R. E. Mahoney, and U. Helmke: Numerical gradient algorithms for eigenvalues and singular value calculation, SIAM J. Matrix Anal. Applic., 17:881-902, 1994.
  248. H. Munthe-Kaas: Lie-Butcher theory for Runge-Kutta methods, BIT, 35(4):572-587, 1995.
  249. H. Munthe-Kaas: Runge-Kutta methods on Lie groups, BIT, 38(1):92-111, 1998.
  250. H. Munthe-Kaas: High order Runge-Kutta methods on manifolds, Appl. Numer. Math., 29:115-127, 1999.
  251. H. Munthe-Kaas and M. Haveraaen: Coordinate free numerics - Part I: How to avoid index wrestling in tensor computations, Technical Report No. 101, Department of Informatics, University of Bergen, Norway, 1995.
  252. H. Munthe-Kaas and M. Haveraaen: Coordinate free numerics - Closing the gap between 'Pure' and 'Applied' mathematics?, In Proceedings of ICIAM-95, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Berlin, 1996. Akademie Verlag.
  253. H. Munthe-Kaas and B. Owren: Computations in a free Lie algebra, Phil. Trans. Royal Soc. A, 357:957-981, 1999.
  254. H. Munthe-Kaas, G. R. W. Quispel, and A. Zanna: Generalized polar decompositions on Lie groups with involutive automorphisms, Foundations of Computational Mathematics, 1(3):297-324, 2001.
  255. H. Munthe-Kaas and A. Zanna: Numerical integration of differential equations on homogeneous manifolds, In F. Cucker and M. Shub, editors, Foundations of Computational Mathematics, pages 305-315. Springer Verlag, 1997.
  256. A. Murua and J. M. Sanz-Serna: Order conditions for numerical integrators obtained by composing simpler integrators, Phil. Trans. Royal Soc. A, 357:1079-1100, 1999.
  257. A. Murua, J. M. Sanz-Serna, and R. D. Skeel: Order conditions for numerical integrators obtained by composing simpler methods, Technical Report 1997/7, Departemento de Matematica Aplicada y Computatión, Universidad de Valladolid, Spain, 1997.
  258. I. M. Navon: Implementation of a posteriori methods for enforcing conservation of potential enstrophy and mass in discrete shallow-water equations models, Monthly Weather Rev., 109:946-958, 1981.
  259. P. Nettesheim and C. Schütte: Numerical integrators for quantum-classical molecular dynamics, Technical report, Konrad Zuse Zentrum Berlin, 1997.
  260. K. Nipp: Numerical integration of differential algebraic systems and invariant manifolds, BIT, 42(2):408-439, 2002.
  261. P. J. Olver: Applications of Lie Groups to Differential Equations, GTM 107. Springer-Verlag, Second edition, 1993.
  262. P. J. Olver: Equivalence, Invariants, and Symmetry, Cambridge University Press, 1995.
  263. B. Orel: Extrapolated Magnus methods, BIT, 41(5):1089-1100, 2001.
  264. J. A. Oteo: The Baker-Campbell-Hausdorff formula and nested commutator identities, J. of Math. Phys., 32(2):419-424, 1991.
  265. B. Owren and A. Marthinsen: Runge-Kutta methods adapted to manifolds and based on rigid frames, BIT, 39(1):116-142, 1999.
  266. B. Owren and A. Marthinsen: Integration methods based on canonical coordinates of the second kind, Numer. Math., 87(4):763-790, 2001.
  267. B. Owren and B. Welfert: The Newton iteration on Lie groups, BIT, 40(1):121-145, 2000.
  268. F. C. Park and B. Ravani: Bézier curves on Riemannian manifolds and Lie groups with kinematic applications, ASME J. of Mech. Design, 117:36-40, 1995.
  269. G. W. Patrick: Two Axially Symmetric Coupled Rigid Bodies: Relative Equilibria, Stability, Bifurcations, and a Momentum Preserving Symplectic Integrator, PhD thesis, University of California at Berkeley, 1991.
  270. G. W. Patrick: Dynamics near stable relative equilibria at non-generic momenta: a numerical investigation, Technical report, Department of Mathematics and Statistics, University of Saskatchewan, 1994.
  271. A. M. Perelemov: Integrable Systems of Classical Mechanics and Lie Algebras, Birkh"auser, 1990.
  272. T. Politi: A formula for the exponential matrix of a real skew-symmetric matrix of order 4, BIT, 41(4):842-845, 2001.
  273. M. Puta: Hamiltonian Mechanical Systems and Geometric Quantization, Kluwer, 1993.
  274. M.-Z. Qin and W.-J. Zhu: Volume-preserving schemes and numerical experiments, Computers Math. Applic., 26:33-42, 1993.
  275. G. R. W. Quispel: Volume-preserving integrators, Physics Letters A, 206:26-30, 1995.
  276. G. R. W. Quispel and H. W. Capel: Solving ODE's numerically while preserving a first integral, Physics Letters A, 218:223-228, 1996.
  277. G. R. W. Quispel and C. Dyt: Solving ODE's numerically while preserving symmetries, Hamiltonian structure, phase space volume, or first integrals, In A. Sydow, editor, Proceedings of the 15th IMACS World Congress, pages 601-607. Wissenschaft & Technik, Berlin, 1997.
  278. G. R. W. Quispel and C. P. Dyt: Volume-preserving integrators have linear error growth, Physics Letters A, 202:25-30, 1998.
  279. G. R. W. Quispel and G. S. Turner: Discrete gradient methods for solving ODE's numerically while preserving a first integral, Physics Letters A, 29:L341-L349, 1996.
  280. A. Flø Rasmussen: Solving Lie-type equations numerically with Magnus series, Master's thesis, Department of Mathematics, Norwegian University of Science and Technology, Trondheim, Norway, 1997.
  281. S. Reich: Symplectic integrators for systems of rigid bodies, Fields Inst. Com., 1995.To appear.
  282. S. Reich: Symplectic integration of constrained Hamiltonian systems by composition methods, SIAM J. Numer. Anal., 33:475-491, 1996.
  283. W. C. Rheinboldt: Differential-algebraic systems as differential equations on manifolds, Math. Comp., 43:473-482, 1984.
  284. J. A. G. Roberts and G. R. W. Quispel: Chaos and time-reversal symmetry: Order and chaos in reversible dynamical systems, Phys. Rep., 216:63-177, 1992.
  285. R. Ruth: A canonical integration technique, IEEE Trans. Nucl. Sci., 30:26-69, 1983.
  286. R. Sahadevan, G. B. Byrnes, and G. R. W. Quispel: Linearisation of difference equations using factorisable Lie symmetries, To appear.
  287. J. M. Sanz-Serna: Geometric integration, In The State of the Art in Numerical Analysis (York, 1996), volume 63 of Inst. Math. Appl. Conf. Ser. New Ser., pages 121-143, New York, 1997. Oxford Univ. Press.
  288. J. M. Sanz-Serna and M. P. Calvo: Numerical Hamiltonian Problems, AMMC 7. Chapman & Hall, 1994.
  289. Y. K. Sasaki: Variational design of finite-difference schemes for initial value problems with an integral invariant, J. of Comp. Phys., 21:270-278, 1976.
  290. A. Schett and J. W. Weil: On the solution of some important second order differential equations in physics using Lie series, Acta Phys. Austriaca, 24:368, 1966.
  291. J. Schiff and S. Shnider: Lie groups and error analysis, To appear.
  292. M. Schönert et al: GAP - Groups, Algorithms and Programming, Lehrstuhl D für Mathematik, Aachen, Germany, 3 edition, 1995.
  293. J.-P. Serre: Lie Algebras and Lie Groups, Number 1500 in Lecture Notes in Mathematics. Springer-Verlag, Second edition, 1992.
  294. Q. Sheng: Solving Partial Differential Equations by Exponential Splitting, PhD thesis, Cambridge University, 1989.
  295. J. C. Simo: The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: Intrinsic definition and geometric interpretation, Comput. Methods Appl. Mech. Engrg., 96:189-200, 1992.
  296. J. C. Simo: On a stress resultant geometrically exact shell model. Part VII: Shell intersections with 5/6-DOF finite element formulations, Comput. Methods Appl. Mech. Engrg., 108:319-339, 1993.
  297. J. C. Simo and D. D. Fox: On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization, Comput. Methods Appl. Mech. Engrg., 72:267-304, 1989.
  298. J. C. Simo, D. D. Fox, and T. J. Huges: Formulations of finite elasticity with independent rotations, Comput. Methods Appl. Mech. Engrg., 95:277-288, 1992.
  299. J. C. Simo, D. D. Fox, and M. S. Rifai: On a stress resultant geometrically exact shell model. Part II: The linear theory; computational aspects, Comput. Methods Appl. Mech. Engrg., 73:53-92, 1989.
  300. J. C. Simo, D. D. Fox, and M. S. Rifai: Formulation and computational aspects of a stress resultant geometrically exact shell model, 1990.
  301. J. C. Simo, D. D. Fox, and M. S. Rifai: On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory, Comput. Methods Appl. Mech. Engrg., 79:21-71, 1990.
  302. J. C. Simo and O. Gonzalez: Recent results on the numerical integration of infinite-dimensional Hamiltonian systems.
  303. J. C. Simo and O. Gonzalez: Assessment of energy-momentum and symplectic schemes for stiff dynamical systems, American Society of Mechanical Engineers, ASME Winter Annual Meeting, New Orleans, Louisiana, 1993.
  304. J. C. Simo and J. Kennedy: On a stress resultant geometrically exact shell model. Part V: Nonlinear plasticity: Formulation and integration algorithms, Comput. Methods Appl. Mech. Engrg., 96:133-171, 1992.
  305. J. C. Simo, T. A. Posbergh, and J. E. Marsden: Stability of coupled rigid body and geometrically exact rods: Block diagonalization and the energy-momentum method, Phys. Rep., 193(6):279-360, 1990.
  306. J. C. Simo, M. S. Rifai, and D. D. Fox: On a stress resultant geometrically exact shell model. Part IV: Variable thickness shells with through-the-thickness stretching, Comput. Methods Appl. Mech. Engrg., 81:91-126, 1990.
  307. J. C. Simo, M. S. Rifai, and D. D. Fox: On a stress resultant geometrically exact shell model. Part VI: Nonlinear dynamics and conserving algorithms, Internat. J. Numer. Methods Engrg., 34:117-164, 1990.
  308. J. C. Simo and N. Tarnov: The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics, Z. Angew. Math. Phys., 43:757-793, 1992.
  309. J. C. Simo and N. Tarnov: A new energy-momentum method for the dynamics of nonlinear shells, Internat. J. Numer. Methods Engrg., 1992.
  310. J. C. Simo, N. Tarnov, and M. Doblaré: Exact energy-momentum algorithms for the dynamics of nonlinear rods, Internat. J. Numer. Methods Engrg., 1993.
  311. J. C. Simo, N. Tarnov, and M. Doblaré: Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms, Internat. J. Numer. Methods Engrg., 38(9):1431-1473, 1995.
  312. J. C. Simo and N. Tarnow: A new energy and momentum conserving algorithm for the non-linear dynamics of shells, Internat. J. Numer. Methods Engrg., 37(15):2527-2549, 1994.
  313. J. C. Simo, N. Tarnow, and K. K. Wong: Exact energy momentum conserving algorithms and symplectic schemes for nonlinear dynamics, Comput. Methods Appl. Mech. Engrg., 1:63-116, 1992.
  314. J. C. Simo and L. Vu-Quoc: A beam model including shear and torsional warping distorsions based on an exact geometric description of nonlinear deformations, Internat. J. Solids Structures, 1987.
  315. J. C. Simo and L. Vu-Quoc: On the dynamics of finite-strain rods undergoing large motions - a geometrically exact approach, Comput. Methods Appl. Mech. Engrg., 66:125-161, 1988.
  316. J. C. Simo and K. K. Wong: Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum, Internat. J. Numer. Methods Engrg., 31:19-52, 1991.
  317. J. C. Simo and K. K. Wong: Addendum: "Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum", Internat. J. Numer. Methods Engrg., 33(6):1321-1323, 1992.
  318. S. T. Smith: Dynamical systems that perform the singular value decomposition, Systems & Control Letters, 16:319-327, 1991.
  319. S. Steinberg: Factored product expansions of solutions of nonlinear differential equations, SIAM J. Math. Anal., 15:108-115, 1984.
  320. S. Steinberg: Lie series and nonlinear ordinary equations, J. of Math. Anal. and Appl., 101:39-63, 1984.
  321. D. M. Stofer: Some Geometric and Numerical Methods for Perturbed Integrable Systems, PhD thesis, ETH Zürich, 1988.
  322. M. Suzuki: New scheme of hybrid exponential product with applications to quantum Monte-Carlo simulations, In D. P. Landau, K. K. Mon, and H.-B. Schütte, editors, Computer Simulation Studies in Condensed Matter Physics IX, pages 1-6. Springer-Verlag, 1995.
  323. N. Tarnow and J. C. Simo: How to render second order accurate time-stepping algorithms fourth order accurate while retaining their stability and conservation properties, Comput. Methods Appl. Mech. Engrg., 115:233-253, 1994.
  324. J. Tuomela: On singular points of quasilinear differential and differential-algebraic equations, Technical Report A369, Institute of Mathematics, Helsinki University of Technology, 1996.
  325. J. Tuomela: On the numerical solution of involutive ordinary differential systems, Technical Report A363, Institute of Mathematics, Helsinki University of Technology, 1996.
  326. J. Tuomela: On singular points of quasilinear differential and differential-algebraic equations, BIT, 37(4):968-977, 1997.
  327. J. Tuomela: On the resolution of singularities of ordinary differential systems, Technical Report A388, Institute of Mathematics, Helsinki University of Technology, 1997.
  328. M. A. A. van Leeuwen: LiE, a software package for Lie group computations, Euromath Bulletin, 1(2), 1994.
  329. V. S. Varadarajan: Lie Groups, Lie Algebras, and Their Representations, GTM 102. Springer-Verlag, 1984.
  330. Dao-Liu Wang: Symplectic difference schemes for Hamiltonian systems on Poisson manifolds, Technical report, Academia Senica, Computing Center, Beijing, China, 1988.
  331. F. W. Warner: Foundations of Differentiable Manifolds and Lie Groups, GTM 94. Springer-Verlag, 1983.
  332. J. Wendlandt and J. Marsden: Mechanical integrators derived from a discrete variational principle, Physica D, 106:223-246, 1997.
  333. J. Wensch: Extrapolation methods in Lie groups, Numer. Math., 89(3):591-604, 2001.
  334. J. Wensch and F. Casas: Extrapolation in Lie groups with approximated BCH-formula, Appl. Numer. Math., 42(1-3):465-472, 2002.
  335. A. Zanna: The method of iterated commutators for ordinary differential equations on Lie groups, Technical Report 1996/NA12, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1996.
  336. A. Zanna: Lie-group methods for isospectral flows, Technical Report 1997/NA02, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1997.
  337. A. Zanna: The Fer expansion and time symmetry: a Strang-type approach, Technical Report 1998/NA14, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1998.
  338. A. Zanna: On the Numerical Solution of Isospectral Flows, PhD thesis, University of Cambridge, England, 1998.
  339. A. Zanna: Collocation and relaxed collocation for the Fer and the Magnus expansions, SIAM J. Numer. Anal., 36(4):1145-1182, 1999.
  340. A. Zanna: Recurrence relation for the factors in the polar decomposition on Lie groups, Technical Report No. 192, Department of Informatics, University of Bergen, Norway, 2000.
  341. A. Zanna, K. Engø, and H. Z. Munthe-Kaas: Adjoint and selfadjoint Lie-group methods, BIT, 41(2):395-421, 2001.
  342. A. Zanna and H. Munthe-Kaas: Iterated commutators, Lie's reduction method and ordinary differential equations on matrix Lie groups, In F. Cucker and M. Shub, editors, Foundation of Computational Mathematics, pages 434-441. Springer-Verlag, 1997.
  343. A. Zanna and H. Z. Munthe-Kaas: Generalized polar decompositions for the approximation of the matrix exponential, Technical Report No. 200, Department of Informatics, University of Bergen, Norway, 2000.
  344. V. Zeitlin: Finite-mode analogs of 2D ideal hydrodynamics: Coadjoint orbits and local canonical structure, Physica D, 49:353-362, 1991.
  345. W. Zhu and M. Qin: Poisson schemes for Hamiltonian systems on Poisson manifolds, Computers Math. Applic., 27:7-16, 1994.
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