Partners NTNU Department of Mathematical Sciences N-7491 Trondheim Norway University of Bergen Department of Informatics N-5020 Bergen Norway

Sponsors The Norwegian Research Council

Publications from the SYNODE project

57. H. Berland and B. Owren Algebraic Structures on Ordered Rooted Trees and Their Significance to Lie Group Integrators, preprint Numerics no 3/2003, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
56. F. Casas and B. Owren Cost efficient Lie group integrators in the RKMK class , preprint Numerics no 5/2002, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
55. E. Celledoni and S. Fiori Neural Learning by Geometric Integration of Reduced Rigid Body Equations , preprint Numerics no 4/2002, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
54. E. Celledoni, A. Marthinsen and B. Owren: Commutator-free Lie group methods , preprint Numerics no 1/2002, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
53. E. Celledoni and B. Owren: On the implementation of Lie group methods on the Stiefel manifold , preprint Numerics no 9/2001, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
52. S. Krogstad: A low complexity Lie group method on the Stiefel manifold, Preprint Department of Informatics, University of Bergen, July 2001. (pdf-format)
51. E. Celledoni and B. Owren: A class of low complexity intrinsic schemes for orthogonal integration, preprint Numerics no 1/2001, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
50. V. Dorodnitsyn, R. Kozlov and P. Winternitz: Second order ordinary difference equations with symmetries: Lagrangian formalism, first integrals and exact solutions
49. R. Kozlov: Conservation laws of semidiscrete canonical Hamiltonian equations, preprint Numerics No. 4/2000, The Norwegian University of Science and Technology, Trondheim, Norway. Published in J. Phys. A: Math. Gen. 34(17):3651-3669, 2001
48. R. Kozlov: Conservation laws of semidiscrete Hamiltonian equations, preprint Numerics No. 3/2000, The Norwegian University of Science and Technology, Trondheim, Norway. Published in J. Math. Phys 42(4):1708-1727, 2001
47. K. Engø: Partitioned Runge-Kutta methods in Lie-group setting, Technical Report no. 202, September 2000, Department of Informatics, University of Bergen.
46. K. Engø: On the BCH-formula in so(3), Technical Report no. 201, September 2000, Department of Informatics, University of Bergen.
45. A. Zanna and H. Z. Munthe-Kaas: Generalized polar decompositions for the approximation of the matrix exponential, Technical Report no. 200, August 2000, Department of Informatics, University of Bergen.
44. A. Zanna: Recurrence relation for the factors in the polar decomposition on Lie groups, Technical Report no. 192, May 2000, Department of Informatics, University of Bergen.
43. 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
42. H. Munthe-Kaas, G. R. W. Quispel and A. Zanna: The polar decomoposition on Lie groups with involutive automorphisms, Technical Report no. 191, May 2000, Department of Informatics, University of Bergen.
41. A. Iserles, H.Z. Munthe-Kaas, S.P. Nørsett and A. Zanna: Lie-group methods, Acta Numerica 9, CUP, 215--365, 2000.
40. K. Engø and A. Marthinsen: Time-Symmetry of the Crouch-Grossman Method, preprint Numerics No. 2/2000, The Norwegian University of Science and Technology, Trondheim, Norway.
39. M. Günther, A. Kværnø and P. Rentrop: Multirate partitioned Runge-Kutta Methods, Preprint Nr. 99/12 Institute für Wissenschaftliches Rechen und Mathematische Modellbildung, Universität Karlsruhe, Karlsruhe, Germany.
38. A. Kværnø: Stability of multirate Runge-Kutta schemes, The Tenth International Colloquium on Differential Equations in Plovdiv, Bulgaria, August 1999.
37. K. Engø and A. Marthinsen: A Note on the Numerical Solution of the Heavy Top Equations, Multibody System Dynamics 5(4):387-397, 2001
36. E. Celledoni, A. Iserles, S.P. Nørsett and B. Orel: Complexity theory for Lie-group solvers, technical report 1999/NA20, DAMTP, Cambridge, UK. To appear in Journal of Complexity.
35. V. Dorodnitsyn, R. Kozlov and P. Winternitz: On Lie group classification of second-order ordinary difference equations, In M. Boiti and F. Pempinelli, editors, Nonlinearity, integrability and all that, Gallipoli, Italy, 1999. World Scientific, Singapore, 1999.
34. K. Engø and S. Faltinsen: Numerical integration of Lie-Poisson systems while preserving coadjoint orbits and energy, Reports in Informatics No. 179, October 1999, Department of Informatics, University of Bergen, Norway. Published in SIAM J. Numer. Anal. 39(1):128-145, 2001
33. E. Celledoni and B. Owren: Lie group methods for rigid body dynamics and time integration on manifolds, to appear in special issue of Comput. meth. in Appl. Mech. and Engrg. (pdf-format). Revised version May 2001 (.ps)
32. V. Dorodnitsyn, R. Kozlov and P. Winternitz: Lie group classification of second-order ordinary difference equations, J. Math. Phys. 41(1):480-504, 2000
31. R. Kozlov and B. Owren: Order reduction in operator splitting methods, preprint Numerics No. 6/1999, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
30. A. Kværnø and B. Leimkuhler: Time Reversible N-Body Integrators Based on Smooth Switches, SIAM J. Sci. Comp. 22(3):1016-1035 (pdf-format)
29. B. Owren and A. Marthinsen: Integration methods based on canonical coordinates of the second kind, preprint Numerics No. 5/1999, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format). Published in Numer. Math. 87(4):763-790, 2001
28. Z. Jackiewicz, A. Marthinsen and B. Owren: Construction of Runge-Kutta Methods of Crouch-Grossman Type of High Order, preprint Numerics No. 4/1999, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format). Published in Adv. Comput. Math. 13(4):405-415, 2000
27. E. Celledoni and A. Iserles: Methods for the approximation of the matrix exponential in a Lie-algebraic setting, Technical Report MSRI 1999-015 (pdf-format). Published in IMA J. Numer. Anal. 21(2):463-488, 2001
26. K. Engø, A. Marthinsen and H. Z. Munthe-Kaas: DiffMan User's Guide, Version 1.6, Technical Report No. 166, March 1999, Department of Informatics, University of Bergen, Norway (pdf-format)
25. A. Zanna, K. Engø and H. Z. Munthe-Kaas: Adjoint and selfadjoint Lie-group methods, technical report 1999/NA02, DAMTP, Cambridge, UK (pdf-format). Published in BIT 41(2):395-421, 2001
24. A. Kværnø and P. Rentrop: Low Order Multirate Runge-Kutta Methods in Electric Circuit Simulation, preprint Numerics No. 2/1999, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
23. S. Faltinsen, A. Marthinsen and H. Z. Munthe-Kaas: Multistep Methods Integrating Ordinary Differential Equations on Manifolds, preprint Numerics No. 3/1999, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
22. 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, February 1999, Department of Informatics, University of Bergen, Norway (pdf-format)
21. A. Marthinsen and B. Owren: Quadrature Methods Based on the Cayley Transform, preprint Numerics No. 1/1999, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
20. V. Dorodnitsyn and R. Kozlov: Second-order ordinary difference equations admitting Lie-point transformations, preprint Numerics No. 3/1998, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
19. A. Iserles, S. P. Nørsett and A. F. Rasmussen: Time-Symmetry and High-Order Magnus Methods, Technical Report 1998/NA06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England
18. K. Engø: On the construction of geometric integrators in the RKMK class, Technical Report No. 158, October 1998, Department of Informatics, University of Bergen, Norway (pdf-format). Published in BIT 40(1):41-61, 2000
17. A. Marthinsen and B. Owren: A Note on the Construction of Crouch-Grossman Methods, preprint Numerics No. 2/1998, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format). Published in BIT 41(1):207-214, 2001
16. A. Marthinsen: Interpolation in Lie Groups and Homogeneous Spaces, Technical Report No. 139, Department of Mathematics, Arizona State University, Tempe, Arizona, 1998 (pdf-format). Published in SIAM J. Numer. Anal. 37(1):269-285, 1999
15. H. Munthe-Kaas and B. Owren: Computations in a Free Lie Algebra, Technical Report No. 148, Department of Informatics, University of Bergen, 1998 (pdf-format). Published in Phil. Trans. Royal Soc. A, 357:957-981, 1999
14. A. Iserles, A. Marthinsen and S. P. Nørsett: On the implementation of the method of Magnus series for linear differential equations, preprint Numerics No. 1/1998, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format). Published in BIT 39(2):281-304, 1999
13. V. A. Dorodnitsyn and R. V. Kozlov: The whole set of symmetry preserving discrete versions of a heat transfer equation with a source, preprint Numerics No. 4/1997, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format)
12. M. I. Bakirova, V. A. Dorodnitsyn and R. V. Kozlov: Symmetry preserving difference schemes for some heat transfer equations, J. Phys. A: Math. Gen. 30:8139-8155, 1997
11. H. Munthe-Kaas: High Order Runge-Kutta Methods on Manifolds, Applied Numerical Mathematics, 29:115-127, 1999 (pdf-format)
10. 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 (pdf-format)
9. K. Engø and A. Marthinsen: Modeling and Solution of some Mechanical Problems on Lie Groups, Multibody System Dynamics 2:71-88, 1998 (pdf-format)
8. A. Iserles and S. P. Nørsett: On the Solution of Linear Differential Equations on Lie Groups, preprint Numerics No. 2/1997, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format). Published in Phil. Trans. Royal Soc. A 357:983-1020, 1999
7. B. Owren and A. Marthinsen: Runge-Kutta Methods Adapted to Manifolds and Based on Rigid Frames, BIT 39(1):116-142, 1999 (pdf-format)
6. B. Owren and B. Welfert: The Newton Iteration on Lie Groups, preprint Numerics No. 3/1996, The Norwegian University of Science and Technology, Trondheim, Norway (pdf-format). Revised version, 09/99 (pdf-format). Published in BIT, 40:121-145, 2000
5. H. Munthe-Kaas and A. Zanna: Numerical Integration of Differential Equations on Homogeneous Manifolds, in Foundation of Computational Mathematics, F. Cucker (editor), pages 305-315, Springer Verlag, 1997 (pdf-format)
4. A. Zanna and H. Munthe-Kaas: Iterated Commutators, Lie's Reduction Method and Ordinary Differential Equations on Matrix Lie Groups, in Foundation of Computational Mathematics, F. Cucker (editor), pages 434-441, Springer Verlag, 1997 (pdf-format)
3. 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. This is an extended version of a paper printed in Applied Modelling and Simulation - Proceedings of the 38th SIMS Simulation Conference, T. Iversen (editor), pp. 231-242, Tapir trykkeri, Norway, 1996 (pdf-format)
2. H. Munthe-Kaas: Runge-Kutta methods on Lie groups, BIT, 38:92-111, 1998 (pdf-format)
1. H. Munthe-Kaas: Lie-Butcher Theory for Runge-Kutta Methods, BIT, 35:572-587, 1995 (pdf-format)

Other papers written with support from the SYNODE project

3. 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 (pdf-format)
2. A. Zanna: Lie-group Methods for Isospectral Flows, Technical Report 1997/NA02, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England (pdf-format)
1. 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 (pdf-format)