List of SYNODE References on

Symplectic Integration

The SYNODE Project is interested in references on the subject Symplectic Integration, and would appreciate to be notified about new (or old) publications in this field. Please mail to Brynjulf.Owren[+]math.ntnu.no.
The list below is available as a BibTeX file.
  1. S. S. Abdullaev: A new integration method of Hamiltonian systems by symplectic maps, J. Phys. A: Math. Gen., 32(15):2745-2766, 1999.
  2. S. S. Abdullaev: The Hamilton-Jacobi method and Hamiltonian maps, J. Phys. A: Math. Gen., 35(12):2811-2832, 2002.
  3. L. Abia and J.M. Sanz-Serna: Partitioned Runge-Kutta methods for separable Hamiltonian problems, Math. Comp., 60:617-634, 1993.
  4. P. G. Akishin, I. V. Puzynin, and S. I. Vinitsky: A hybrid numerical method for analysis of dynamics of classical Hamiltonian systems, Computers Math. Applic., 34:45-73, 1997.
  5. M. Alvarez and J. Delgado: The spring-pendelum system, In E. A. Lacomba and J. Llibre, editors, Hamiltonian Systems and Celestical Mechanics, pages 1-14. World Scientific Publishing, 1993.
  6. D.V. Anosov and V.I. Arnold: Dynamical Systems I, Springer, Berlin, 1988.
  7. A. L. Araujo, A. Murua, and J. M. Sanz-Serna: Symplectic Methods Based on Decompositions, SIAM J. Numer. Anal., 34(5):1926-1947, 1997.
  8. V.I. Arnold: Mathematical Methods of Classical Mechanics, Springer, New York, 2nd edition, 1988.
  9. U. Ascher and S. Reich: On some difficulties in integrating highly oscillatory Hamiltonian system, Technical report, Department of Computer Science, University of British Columbia, 1997.
  10. U. M. Ascher and S. Reich: The midpoint scheme and variants for Hamiltonian systems: advantages and pitfalls, To appear.
  11. A. Aubry and P. Chartier: Pseudo-symplectic Runge-Kutta methods, Technical report, IRISA, 1997.
  12. A. Aubry and P. Chartier: A Note on Pseudo-Symplectic Runge-Kutta Methods, BIT, 38(4):802-806, 1998.
  13. S. P. Auerbach and A. Friedman: Long-time behavior of numerically computed orbits: Small and intermediate timestep analysis of one-dimensional systems, J. of Comp. Phys., 93:189-223, 1991.
  14. E. Barth and B. Leimkuhler: Symplectic Methods for Conservative Multibody Systems, Fields Inst. Com., 1995.To appear.
  15. E. Barth and B. Leimkuhler: A semi-explicit, variable-step size integrator for constrained dynamics, To appear, 1996.
  16. E. Barth and B. Leimkuhler: Symplectic Methods for Conservative Multibody Systems, In J. E. Mardsen, G. W. Patrick, and W. F. Shadwick, editors, Integration Algorithms and Classical Mechanics, pages 25-44. American Mathematical Society, 1996.
  17. S. Benzel, Ge Zhong, and C. Scovel: Elementary construction of higher order Lie-Poisson integrators, Physics Letters A, 174:229-232, 1993.
  18. W.J. Beyn: Numerical methods for dynamical systems, In W. Light, editor, Advances in Numerical Analysis, volume I, pages 175-236. Clarendon Press, Oxford, 1991.
  19. J.J. Biesiadecki and R.D. Skeel: Dangers of multiple-time-step methods, J. of Comp. Phys., 109:318-328, 1993.
  20. K.E. Brenan, S.L. Campbell, and L.R. Petzold: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York, 1989.
  21. R. Brouzet, R. Caboz, J. Rabenivo, and V. Ravonson: Two-degrees of freedom quasi Bi-Hamiltonian systems, Physics Letters A, 29:2069-2076, 1996.
  22. K. Burrage and J.C. Butcher: Stability criteria for implicit Runge-Kutta methods, SIAM J. Numer. Anal., 16:46-57, 1979.
  23. J.C. Butcher: Implicit Runge-Kutta Processes, Math. Comp., 18:50-64, 1964.
  24. J.C. Butcher: The Numerical Analysis of Ordinary Differential Equations, John Wiley, Chichester, 1987.
  25. R. Caboz, V. Ravonson, and L. Gavrilov: Bi-Hamiltonian structure of an integrable Hénon-Heiles system, J. Phys. A, 24:L523-L525, 1991.
  26. M. P. Calvo: High order starting iterates for implicit Runge-Kutta methods: an improvement for variable-step symplectic integrators, IMA J. Numer. Anal., 22(1):153-166, 2002.
  27. M. P. Calvo, A. Iserles, and A. Zanna: Runge-Kutta methods on manifolds, Technical Report DAMPT 1995/NA7, University of Cambridge, 1995.
  28. M. P. Calvo, A. Murua, and J. M. Sanz-Serna: Modified Equations for ODE's, In Chaotic Numerics, number 172 in Contemporary Mathematics, pages 1-30. American Mathematical Society, 1994.
  29. M.P. Calvo: Characterization of Symplectic Runge-Kutta-Nyström Methods, In Proceedings of the XII Congress on Differential Equations and Applications, pages 111-115. University of Oviedo, Oviedo, 1991.
  30. M.P. Calvo: Métodos Runge-Kutta-Nyström Simplécticos, PhD thesis, Universidad de Valladolid, 1992.
  31. M.P. Calvo and E. Hairer: Accurate Long-Term Integration of Dynamical Systems, Numer. Math., 18:95-105, 1995.
  32. M.P. Calvo and E. Hairer: Further Reduction in the Number of Independent Order Conditions for Symplectic, Explicit Partitioned Runge-Kutta and Runge-Kutta-Nyström Methods, Appl. Numer. Math., 18:107-114, 1995.
  33. M.P. Calvo and J.M. Sanz-Serna: Order conditions for canonical Runge-Kutta-Nyström methods, BIT, 32:131-142, 1992.
  34. M.P. Calvo and J.M. Sanz-Serna: Variable steps for symplectic integrators, In D.F. Griffiths and G.A. Watson, editors, Numerical Analysis, 1991, pages 34-48. Longman, London, 1992.
  35. M.P. Calvo and J.M. Sanz-Serna: The development of variable-step symplectic integrators with application to the two-body problem, SIAM J. Sci. Comput., 14:936-952, 1993.
  36. M.P. Calvo and J.M. Sanz-Serna: High-order symplectic Runge-Kutta-Nyström methods, SIAM J. Sci. Comput., 114:1237-1252, 1993.
  37. M.P. Calvo and J.M. Sanz-Serna: Reasons for failure. The integration of the two-body problem with a symplectic Runge-Kutta-Nyström code with stepchanging facilities, In C. Perelló, C. Simo, and J. Sola-Morales, editors, Equadiff 91, pages 34-48. World Scientific, Singapore, 1993.
  38. M.P. Calvo and J.M. Sanz-Serna: Canonical B-Series, Numer. Math., 67:161-175, 1994.
  39. J. Candy and W. Rozmus: A symplectic integration algorithm for separable Hamiltonian functions, J. of Comp. Phys., 92:230-256, 1991.
  40. B. Cano and J. M. Sanz-Serna: Error Growth in the Numerical Integration of Periodic Orbots, with Application to Hamiltonian and Reversible Systems, SIAM J. Numer. Anal., 34(4), 1997.
  41. F. Casas: Fer's Factorization as a Symplectic Integrator, Numer. Math., 74(3):283-303, 1996.
  42. R. P. K. Chan: On symmetric Runge-Kutta methods of high order, Computing, 45:301-309, 1990.
  43. P. J. Channel: Symplectic integration algorithms, Technical Report AT-6:ATN 83-9, Los Alamos National Laboratory, 1983.
  44. P. J. Channel and J. S. Scovel: Integrators for Lie-Poisson dynamical systems, Physica D, 50:80-88, 1991.
  45. P. J. Channell and F. R. Neri: An Introduction to Symplectic Integrators, In J. E. Mardsen, G. W. Patrick, and W. F. Shadwick, editors, Integration Algorithms and Classical Mechanics, pages 45-58. American Mathematical Society, 1996.
  46. P.J. Channell and C. Scovel: Symplectic integration of Hamiltonian systems, Nonlinearity, 3:231-259, 1990.
  47. R. Chatterjee: Dynamical symmetries and Nambu mechanics, Letters in Mathematical Physics, 36:117-126, 1996.
  48. S. A. Chin: Symplectic integrators from composite operator factorization, Physics Letters A, 226:344-348, 1997.
  49. G. J. Cooper: Stability of Runge-Kutta Methods for Trajectory Problems, IMA J. Numer. Anal., 7:1-13, 1987.
  50. G.J. Cooper and R. Vignesvaran: A scheme for the implementation of implicit Runge-Kutta methods, Computing, 45:321-332, 1990.
  51. C. Cronström and M. Noga: Multi-Hamiltonian structure of the Lotka-Volterra and quantum Volterra models, Nuclear Physics B, 445:501-515, 1995.
  52. M. Crouzeix: Sur la B-stabilité des méthodes de Runge-Kutta, Numer. Math., 32:75-82, 1979.
  53. G. Dahlquist: Error analysis for a class of methods for stiff nonlinear initial value problems, In G.A. Watson, editor, Numerical Analysis, Dundee, 1975, pages 60-74. Springer, Berlin, 1975.
  54. J. de Frutos, T. Ortega, and J.M. Sanz Serna: A Hamiltonian explicit algorithm with spectral accuracy for the ``good'' Boussinesq equation, Comput. Methods Appl. Mech. Engrg., 80:417-423, 1990.
  55. J. de Frutos and J. M. Sanz-Serna: Erring and being Conservative, In Numerical Analysis 1993, volume 303 of Pitman Res. Notes Math. Ser., pages 75-88. Longman Sci. Tech., Harlow, 1994.
  56. J. de Frutos and J. M. Sanz Serna: Accuracy and Conservation Properties in Numerical Integration: The Case of the Korteweg-de Vries Equation, Numer. Math., 75:421-446, 1997.
  57. J. de Frutos and J.M. Sanz Serna: An easily implementable fourth-order method for the time integration of wave problems, J. of Comp. Phys., 103:160-168, 1992.
  58. K. Dekker and J.G. Verwer: Stability of Runge-Kutta Methods for Stiff Initial Value Problems, North-Holland, Amsterdam, 1984.
  59. J. R. Dormand and P. J. Prince: Practical Runge-Kutta processes, SIAM J. Sci. Comput., 10:977-989, 1989.
  60. J.R. Dormand, M.E.A. El-Mikkawy, and P.J. Prince: Families of Runge-Kutta-Nyström formulae, IMA J. Numer. Anal., 7:235-250, 1987.
  61. J.R. Dormand, M.E.A. El-Mikkawy, and P.J. Prince: High-order embedded Runge-Kutta-Nyström formulae, IMA J. Numer. Anal., 11:297, 1987.
  62. A. J. Dragt and D. T. Abell: Symplectic Maps and Computation of Orbits in Particle Accelerators, In J. E. Mardsen, G. W. Patrick, and W. F. Shadwick, editors, Integration Algorithms and Classical Mechanics, pages 59-86. American Mathematical Society, 1996.
  63. A.J. Dragt and J.M. Finn: Lie series and invariant functions for analytic symplectic maps, J. Nath. Phys., 17:2215-2227, 1976.
  64. A.J. Dragt and E. Forest: Computation of Nonlinear Behavior of Hamiltonian Systems using Lie Algebraic Methods, J. of Math. Phys., 24(12):2734-2744, 1983.
  65. A. Dullweber, B. Leimkuhler, and R. I. McLachlan: Split-Hamiltonian Methods for Rigid Body Molecular Dynamics, Technical Report 1997/NA11, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 1997.
  66. H. M. M. Ten Eikelder: Canonical and Non-canonical Symmetries for Hamiltonian Systems, PhD thesis, Technical University of Eindhoven, 1984.
  67. T. Eirola: Aspects of backward error analysus of numerical ODEs, J. Comput. Appl. Math, 45:65-73, 1993.
  68. T. Eirola: Monotonicity of Quadratic Forms with Symplectic Runge-Kutta Methods, Appl. Numer. Math., 17(3):293-298, 1995.
  69. T. Eirola and J.M. Sanz Serna: Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods, Numer. Math., 61:281-290, 1992.
  70. T. Ergenç and B. Karasözen: Runge-Kutta Collocation Methods for Rigid Body Lie-Poisson Equations, Internat. J. Comput. Math., 62:63-71, 1996.
  71. D. J. Estep and A. M. Stuart: The Rate of Error Growth in Hamiltonian-Conserving Integrators, Z. Angew. Math. Phys., 46(3):407-418, 1995.
  72. K. Feng: On difference schemes and symplectic geometry, In K. Feng, editor, Proceedings of the 1984 Beijing Symposium on Differential Geometry and Differential Equations, pages 42-58. Science Press, Beijing, 1985.
  73. K. Feng: Canonical Difference Schemes for Hamiltonian Canonical Differential Equations, In International Workshop on Applied Differential Equations (Beijing, 1985), pages 59-73. World Sci. Publishing, Singapore, 1986.
  74. K. Feng: Difference schemes for Hamiltonian formalism and symplectic geometry, J. Comput. Math., 4:279-289, 1986.
  75. K. Feng: Symplectic geometry and numerical methods in fluid dynamics, In F.G. Zhuang and Y.L. Zhu, editors, Tenth International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics, pages 1-7. Springer, Berlin, 1986.
  76. K. Feng: The Symplectic Methods for Computation of Hamiltonian Systems, Springer Lecture Notes in Numerical Methods for PDE's, 1987.
  77. K. Feng: The Hamiltonian Way for Computing Hamiltonian Dynamics, Math. Appl., 56:17-35, 1991.
  78. K. Feng and M. Z. Qin: The symplectic methods for the computation of Hamiltonian equations, In Y. L. Zhu and B. Y. Guo, editors, Numerical Methods for Partial Differential Equations, Lecture Notes in Mathematics 1297, pages 1-37. Springer, Berlin, 1987.
  79. K. Feng and M.Z. Qin: Hamiltonian Algorithms for Hamiltonian Dynamical Systems, Progr. Natur. Sci., 1(2):105-116, 1991.
  80. K. Feng and M.Z. Qin: Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study, Comput. Phys. Comm., 65:173-187, 1991.
  81. K. Feng, M.Z. Qin, and D.L. Wang: Construction of canonical difference schemes for Hamiltonian formalism via generating functions, J. Comput. Math., 7:71-96, 1989.
  82. K. Feng and Z.-J. Shang: Volume-preserving algorithms for source-free dynamical systems, Numer. Math., 71:451-463, 1995.
  83. K. Feng and D.L. Wang: A Note on Conservation Laws of Symplectic Difference Schemes for Hamiltonian Systems, J. Comput. Math., 9(3):229-237, 1991.
  84. K. Feng and D.L. Wang: Symplectic Difference Schemes for Hamiltonian Systems in General Symplectic Structure, J. Comput. Math., 9(1):86-96, 1991.
  85. K. Feng and D.H. Yu: Canonical Integral Equations of Elliptic Boundary Value Problems and their Numerical Solutions, In Proceedings of the China-France symposium on finite element methods (Beijing, 1982), pages 211-252. Science Press, Beijing, 1983.
  86. K.Q. Feng, H.M. Wu, and M.Z. Qin: Symplectic Difference Schemes for Linear Hamiltonian Canonical Systems, J. Comput. Math., 8(4):371-380, 1990.
  87. E. Forest: Sixth-order Lie group integrators, J. of Comp. Phys., 99:209-213, 1992.
  88. E. Forest, J. Bengtsson, and M.F. Reusch: Application of the Yoshida-Ruth Techniques to Implicit Integration and Multi-Map Explicit Integration, Physics Letters A, 158:99-101, 1991.
  89. E. Forest and M. Berz: Canonical Integration and Analysis of Periodic Maps using Nonstandard Analysis and Lie Methods, In Lie Methods in Optics, II, Lecture Notes in Physics, pages 47-66. Springer, Berlin, 1989.
  90. E. Forest and R.D. Ruth: Fourth order symplectic integration, Physica D, 43:105-117, 1990.
  91. T. Forester and W. Smith: On Multiple Time-Step Algorithms and the Ewald Sum, Mol. Sim., 13(3):195-204, 1994.
  92. J. Frank, W. Huang, and B. Leimkuhler: Geometric Integrators for Classical Spin Systems, J. of Comp. Phys., 133:160-172, 1997.
  93. B. Garcia-Archilla, J. M. Sanz-Serna, and R. D. Skeel: Long-time-steps methods for oscillatory differential equations, Technical Report 1996/7, Departemento de Matematica Aplicada y Computatión, Universidad de Valladolid, Spain, 1996.To appear in a book to celebrate Prof. A. R. Mitchell's 70th birthday.
  94. B. Garcia-Archilla, J. M. Sanz-Serna, and R. D. Skeel: The Mollified Impulse Method for Oscillatory Differential Equations, Technical Report 1997/5, Universidad de Valladolid, Valladolid, Spain, 1997.
  95. Z. Ge: Equivariant symplectic difference schemes and generating functions, Physica D, 49:376-386, 1991.
  96. Z. Ge: Symplectic integrators for Hamiltonian systems, In W. Cai et al., editor, Numerical Methods in Applied Sciences, pages 97-108, New York, 1995. Science Press.
  97. Z. Ge and K. Feng: On the Approximation of Linear Hamiltonian Systems, J. Comput. Math., 6(1):88-97, 1988.
  98. Z. Ge and J. Marsden: Lie-Poisson integrators and Lie-Poisson Hamiltonian-Jacobi theory, Physics Letters A, 133:134-139, 1988.
  99. Z. Ge and C. Scovel: Hamiltonian truncation of shallow water equations, Technical Report LA-UR-93-1611, Los Alamos National Lab., New Mexico, USA, 1993.
  100. C. W. Gear: Invariants and numerical methods for ODEs, Physica D, 60:303-310, 1992.
  101. T. Geveci: Fundamental difficulties in the numerical analysis of Hamiltonian systems, Technical report, Department of Mathematics, Middle East Technical University, Ankara, Turkey, 1992.
  102. B. Gladman, M. Duncan, and J. Candy: Symplectic integrators for long-term integration in celestial mechanics, Celest. Mech., 52:221-240, 1991.
  103. I. Gladwell, G. Reddien, and J. Wang: Energy superconvergence of one-step methods for separable Hamiltonian systems, Physics Letters A, 209:31-38, 1995.
  104. O. Gonzalez: Time Integration and Discrete Hamiltonian Systems, Technical report, Division of Applied Mathematics, Department of Mechanical Engineering, Stanford University, 1996.To appear in the Journal of Nonlinear Science.
  105. O. Gonzalez, D. J. Higham, and A. M. Stuart: Qualitative properties of modified equations, Technical Report Mathematics Research Report No. 19, University of Strathclyde, 1997.
  106. O. Gonzalez and J. 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.
  107. O. Gonzalez and A. M. Stuart: Remarks on the qualitative properties of modified equations, Division of Applied Mathematics, Stanford University, 1996.
  108. P. Görtz and R. Scherer: Reducibility and Characterization of Symplectic Runge-Kutta Methods, Electronic Transactions on Numerical Analysis, 2:194-204, 1994.
  109. D.F. Griffiths and J.M. Sanz Serna: On the scope of the method of modified equations, SIAM J. Sci. Comput., 7:994-1008, 1986.
  110. H. Grubmüller, H. Heller, A. Windermuth, and K. Schulten: Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-Range Interactions, Mol. Sim., 6:121-142, 1991.
  111. J. Guckenheimer and Ph. Holmes: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer, New York, 1983.
  112. E. Hairer: Backward analysis of numerical integrators and symplectic methods, In K. Burrage, C. Baker, P. v.d. Houwen, Z. Jackiewicz, and P. Sharp, editors, Scientific Computation and Differential Equations, volume 1 of Annals of Numer. Math., pages 107-132, Amsterdam, 1994. J.C. Baltzer.Proceedings of the SCADE'93 conference, Auckland, New-Zealand, January 1993.
  113. E. Hairer: Variable time step integration with symplectic methods, Technical report, Université de G`eneve, Dépt. de mathématiques, 1997.To appear in "Applied Numerical Mathematics".
  114. E. Hairer, Ch. Lubich, and M. Roche: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Springer, Berllin, 1989.
  115. E. Hairer, A. Iserles, and J.M. Sanz Serna: Equilibria of Runge-Kutta methods, Numer. Math., 58:243-254, 1990.
  116. E. Hairer and P. Leone: Order barriers for symplectic multi-value methods, Technical report, Université de G`eneve, Dépt. de mathématiques, 1997.
  117. E. Hairer and C. Lubich: Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization, To appear, 1997.
  118. E. Hairer, A. Murua, and J.M. Sanz Serna: The non-existence of symplectic multi-derivative Runge-Kutta methods, Preprint, 1993.
  119. E. Hairer, S.P. Nørsett, and G. Wanner: Solving Ordinary Differential Equations I, Nonstiff Problems, Springer, Berlin, 1987.
  120. E. Hairer and D. Stoffer: Reversible long-term integration with variable step sizes, Technical report, Dept. of Math., Univ. of Geneva, Switzerland, 1995.
  121. E. Hairer and G. Wanner: On the Butcher group and general multivalue methods, Computing, 13:1-15, 1974.
  122. E. Hairer and G. Wanner: Algebraically stable and implementable Runge-Kutta methods of high order, SIAM J. Numer. Anal., 18:1098-1108, 1981.
  123. E. Hairer and G. Wanner: Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, Springer, Berlin, 1991.
  124. M. Hankel, B. Karasözen, P. Rentrop, and U. Schmitt: A Molecular Dynamics Model for Symplectic Integrators, Mathematical Modelling of Systems, 3(4):282-296, 1997.
  125. D. J. Hardy, D. I. Okunbor, and R. D. Skeel: Symplectic Variable Stepsize Integration for n-Body Problems, To appear, 1997.
  126. M. Hénon and C. Heiles: The applicability of the third integral of motion: some numerical experiments, Astron. J., 69:73-79, 1964.
  127. B. M. Herbst, F. Varadi, and M. J. Ablowitz: Symplectic methods for the nonlinear schrödinger equation, Mathematics and Computers in Simulation, 37:353-369, 1994.
  128. B.M. Herbst and M.J. Ablowitz: Numerical homoclinic instabilities in the sine-Gordon equation, Quaestiones Mathematicae, 15:345-363, 1992.
  129. B.M. Herbst and M.J. Ablowitz: Numerical chaos, symplectic integrators and exponentially small splitting distances, J. of Comp. Phys., 105:122-132, 1993.
  130. M. Hochbruck and C. Lubich: A bunch of time integrators for quantum/classical molecular dynamics, Submitted to Algorithms for Macromolecular Modelling (P. Deuflhard, J. Hermans, B. Leimkuhler, A. Mark, S. Reich and R. D. Skeel, eds.), Springer Lecture Notes in Computational Science and Engineering, 1997.
  131. J. Hofbauer: Evolutionary dynamics for bimatrix games: A Hamiltonian system?, J. Math. Biol, 34:675-688, 1996.
  132. M. Huang: A Hamiltonian approximation to simulate solitary waves of the Korteweg-de Vries equation, Math. Comp., 56:607-620, 1991.
  133. W. Huang and B. Leimkuhler: The adaptive Verlet method, SIAM J. Sci. Comput., 18(1):239, 1997.
  134. D. D. Humphreys, R. A. Friesner, and B. J. Berne: A Multiple-Time-Step Molecular Dynamics Algorithm for Macromolecules, J. Phys. Chem., 98(27):6685-6892, 1994.
  135. A. R. Humpries and A. M. Stuart: Runge-Kutta Methods for Dissipative and Gradient Dynamical Systems, Technical Report NA-92-17, Numerical Analysis Project, Computer Science Department, Stanford University, 1992.
  136. A. Iserles: Stability and dynamics of numerical methods for ordinary differential equations, IMA J. Numer. Anal., 10:1-30, 1990.
  137. A. Iserles: Efficient Runge-Kutta methods for Hamiltonian equations, Bull. Hellenic Math. Soc., 32:3-20, 1991.
  138. A. Iserles: Insight, not just numbers, Technical Report 1997/NA10, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 1997.
  139. A. Iserles and S.P. Nørsett: Order Stars, Chapman & Hall, 1991.
  140. A. Iserles, A.T. Peplow, and A.M. Stuart: A unified approach to spurious solutions introduced by time discretization. Part I: Basic theory, SIAM J. Numer. Anal., 28:1723-1751, 1991.
  141. A. Iserles and A.M. Stuart: A unified approach to spurious solutions introduced by time discretization. Part II: BDF-like methods, IMA J. Numer. Anal., 12:487-501, 1992.
  142. D. Janezic: Symplectic Numerical Methods for Molecular Dynamics Simulation, Biophys. J., 68:A341, 1995.
  143. D. Janezic and F. Merzel: An Efficient Symplectic Integration Algorithm for Molecular Dynamics Simulations, J. of Chem. Inf. and Comp. Sci., 35:321-326, 1995.
  144. D. Janezic and F. Merzel: Molecular Dynamics Simulations of Macromolecules: Improvements on Computational Efficiency, In R. Trobec, M. Vajtersic, P. Zinterhof, J. Silc, and B. Robic, editors, Proceedings of the International Workshop PARALLEL NUMERICS '96, pages 17-27, Ljubljana, Slovenia, 1996. Institut Jozef Stefan.(ISBN 86-80023-25-6).
  145. D. Janezic and F. Merzel: Simulations of Macromolecules: Improvements of MD Efficiency, Progress in Biophy. & Mol. Biol., 65, S1:P-A3-34, 48, 1996.
  146. D. Janezic and B. Orel: Implicit Runge-Kutta Method for Molecular Dynamics Integration, J. of Chem. Inf. and Comp. Sci., 33:252-257, 1993.
  147. D. Janezic and B. Orel: Improvement of Methods for Molecular Dynamics Integration, Int. J. Quant. Chem., 51:407-415, 1994.
  148. D. Janezic and R. Trobec: Parallelization of an Implicit Runge-Kutta Method for Molecular Dynamics Integration, J. of Chem. Inf. and Comp. Sci., 34:641-646, 1994.
  149. L. O. Jay: Runge-Kutta type methods for index three differential-algebraic equations with applications to Hamiltonian systems, PhD thesis, Department of Mathematics, University of Geneva, Switzerland, 1994.
  150. L. O. Jay: Structure-preservation for constrained dynamics with super partitioned additive Runge-Kutta methods, to appear in SIAM J. Sci. Comput., 1996.
  151. L. O. Jay: Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems, SIAM J. Numer. Anal., 33:368-387, 1996.
  152. L. O. Jay: Lagrangian integration with symplectic methods, Technical Report AHPCRC Preprint 97-009, University of Minnesota, 1997.
  153. W. Kahan: Unconventional numerical methods for trajectory calculations, Lecture Notes, CS Division, Department EECS, University at California at Berkeley, 1993.
  154. W. Kahan and R.-C. Li: Unconventional schemes for a class of ordinary differential equations: with applications to the Korteweg-de Vries equation, J. of Comp. Phys., 134:316-331, 1997.
  155. J. Kalayci and Y. Nutku: Bi-Hamiltonian structure of a WDVV equation in 2-d topological field theory, Physics Letters A, 227:177-182, 1997.
  156. F. Kang and Z.J. Shang: Volume-Preserving Algorithms for Source-Free Dynamical Systems, Numer. Math., 75(4):451-463, 1995.
  157. B. Karasözen: Comparison of Reversible Integrators for a Hamiltonian in Normal Form, In E. Kreuzer and O. Mahrenholz, editors, Proceedings of the Third International Congress on Industrial and Applied Mathematics, ICIAM 95, Issue 4: Applied Sciences, especially Mechanics (Minisymposia), pages 563-566, 1996.
  158. B. Karasözen: Composite Integrators for Bi-Hamiltonian Systems, Comp. & Math. with Applic., 32:79-86, 1996.
  159. B. Karasözen: Numerical Studies on a Bi-Hamiltonian Hénon-Heiles System, Technical Report No 133, Middle East Technical University, Department of Mathematics, Ankara, Turkey, 1996.
  160. B. Karasözen: Runge-Kutta methods for Hamiltonian systems in non-standard symplectic two-form, Submitted, 1996.
  161. B. Karasözen: Reflexive methods for dynamical systems with conserved quantities, Technical Report Nr. 1897, Technische Hochschule Darmstadt, FB Mathematik, 1997.
  162. U. Kirchgraber: An ODE-solver based on the method of averaging, Numer. Math., 53:621-652, 1988.
  163. A. Kol, B. Laird, and B. Leimkuhler: A symplectic method for rigid-body molecular simulation, Technical Report 1997/NA5, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 1997.
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This list was automatically generated Sat Mar 23 16:53:48 MET 2002
Brynjulf Owren <bryn[+]math.ntnu.no>