RKMK method of solving non-damping LL equations and ferromagnet chain equations

Applied Mathematics and Computation

Volumn 157, Issue 2, 2004, Pages 407-424

  Sun, Jian Qiang ^a   Ma, Zhong Qi ^a   Qin, Meng Zhao ^b  

^a INSTITUTE OF HIGH ENERGY PHYSICS   (China)

^b INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Ferromagnet chain equations; Non damping LL equations; RKMK methods; Square conservation schemes

Indexed keywords

FERROMAGNET CHAIN EQUATIONS; NON-DAMPING LL EQUATIONS; RKMK METHODS; SQUARE-CONSERVATION SCHEMES;

ALGORITHMS; DAMPING; ITERATIVE METHODS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; RUNGE KUTTA METHODS;

FERROMAGNETISM;

EID: 4444364321     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.08.042     Document Type: Article

References (14)

1. Munthe-Kaas H. High order Runge-Kutta methods on manifolds. Appl. Numer. Math. 29:1999;115-127.
2. Calvo M.P., Iserles A., Zanna A. Runge-Kutta methods for orthogonal and isospectral flows. Appl. Numer. Math. 22:1996;153-163.
3. Iserles A., Munthe-Kaas H., Nørsett S.P. Lie group methods. Acta Numer. 2000;215-365.
4. Qin M.Z. Two difference schemes for the systems of ferromagnetic chain. J. Comp. Math. 1986;11.
5. Crouch P.E., Grossman R. Numerical integration of ordinary differential equations on manifolds. J. Nonlinear Sci. 3:1993;1-33.
6. Zanna A. Collocation and relaxed collocation for the Fer and the Magnus expansion. SIAM J. Numer. Anal. 36:1999;1145-1182.
7. Budd C.J., Iserles A. Geometric integration: numerical solution of differential equations on manifolds. Philos. Trans. R. Soc. Lond., A. 357:1999;945-956.
8. J.A.G. Roberts, C.J. Thompson, Dynamics of the classical Heisenberg spin chain, Technique Report 11-1978, Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia.
9. S. Krogstad, A low complexity Lie group method on the Stiefel manifold, report no, July 2001, department of informatics, University of Bergen, Bergen, Norway.
10. Iserles A. Numerical methods on (and off) manifolds. Cuker F., Shub M. Foundations of Computational Mathematics. 1997;180-189 Springer-Verlag, New York.
11. Varadarajan V.S. Lie Groups, Lie Algebras and their Representations. 1984;Springer-Verlag, Berlin.
12. A. Marthinsen, H. Munthe-Kaas, B. Owren, Simulation of ordinary differential equations on manifolds, Department of Mathemathematical Science, Num, N-7304, Trondheim, Norway.
13. Munthe-Kaas H. Runge-Kutta methods on Lie groups. BIT. 38:1996;92-111.
14. Chen J.B., Munthe-Kass H., Qin M.Z. Square-conservation scheme for a class of evolution equations using Lie-group methods. SIAM J. Numer. Anal. 39(6):2002;216-2178.