Multisymplectic schemes for the nonlinear Klein-Gordon equation

Mathematical and Computer Modelling

Volumn 36, Issue 9-10, 2002, Pages 963-977

  Wang, Yu Shun ^a,b   Qin, Meng Zhao ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b NANJING NORMAL UNIVERSITY   (China)

Author keywords

Multisymplectic schemes; Multisymplectic structure; Nonlinear Klein Gordon equation; Numerical experiments; Variational principle

Indexed keywords

EID: 0037195882     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(02)00250-9     Document Type: Article

References (10)

1. K. Feng and M.Z. Qin, The symplectic methods for computation of Hamiltonian systems, In Proc. Conf. on Numerical Methods for PDEs, Lecture Notes in Math, 1297, (Edited by Y.L. Zhu and B.-Y. Guo), pp. 1-37, Springer, Berlin, (1987).
2. M.Z. Qin, A symplectic difference scheme for the PDEs, AMS/IP Studies in Advanced Mathematics 3, 349-354, (1997).
3. J.E. Marsden and S. Shkoller, Multisymplectic geometry, covariant Hamiltonians, and water waves, Math. Proc. Camb. Phil. Soc 125, (1999).
4. J.E. Marsden, G.P. Patrick and S. Shkoller, Multisymplectic geometry, variational integrators, and nonlinear PDEs, Comm. Math. Phys. 199, 351-395, (1998).
5. T.J. Bridges, Multisymplectic structures and wave propagation, Math. Proc. Camb. Phil. Soc. 121, (1997).
6. S. Reich, Multi-symplectic Runge-Kutta methods for Hamiltonian wave equations, JCP 157, 473-499, (2000).
7. T.J. Bridges and S. Reich, Department of Mathematics and Statistics University of Surrey, In Multisymplectic Integrators: Numerical Schemes for Hamiltonian PDEs That Conserve Symplecticity, (preprint).
8. S. LI and L.V.-Quoc, Finite difference calculus invariant structure of a class algorithms for the nonlinear Klein-Gordon equation, SIAM J. Numer. Anal. 32 (6), 1839-1875, (December 1995).
9. S. Jimenez and L. Vazquez, Analysis of four numerical schemes for a nonlinear Klein-Gordon equation, Applied Mathematics and Computations 35, 61-94, (1990).
10. P.J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, (1986).