Publications from the SYNODE project

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)