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Two energy conserving numerical schemes for the sine-Gordon equation. (English) Zbl 0732.65107
Authors’ summary: Two explicit conservative numerical schemes for the sine-Gordon equation are proposed. Their stability and convergence are proved. Numerical simulation of a sine-Gordon soliton shows that the new schemes are very accurate and fast.

65Z05Applications of numerical analysis to physics
65M12Stability and convergence of numerical methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
Full Text: DOI
[1] Dodd, R. K.; Eibeck, J. C.; Gibbon, J. D.; Morris, H. C.: Solitons and nonlinear wave equations. (1982) · Zbl 0496.35001
[2] Ablowitz, M. J.; Kruskal, M. D.; Ladik, J. F.: Solitary wave collisions. SIAM J. Appl. math. 36, 428-437 (1979) · Zbl 0408.65075
[3] Fucito, F.; Marchesoni, F.; Marinari, E.; Parisi, G.; Peliti, L.; Ruffo, S.; Vulpiani, A.: Approach to equilibrium in a chain of nonlinear oscillators. J. physique 43, 707-713 (1982)
[4] Ben-Yu, Guo; Pascual, P. J.; Rodriguez, M. J.; Vázquez, L.: Numerical solution of the sine-Gordon equation. Appl. math. Comput. 18, 1-14 (1986) · Zbl 0622.65131
[5] Strauss, W. A.; Vázquez, L.: Numerical solution of a nonlinear Klein-Gordon equation. J. comput. Phys. 28, 271-278 (1978) · Zbl 0387.65076
[6] Jiménez, S.; Vázquez, L.: Analysis of four numerical schemes for a nonlinear Klein-Gordon equation. Appl. math. Comput. 35, 61-95 (1990) · Zbl 0697.65090
[7] Fei, Zhang; Vázquez, Luis: Some conservative numerical schemes for an ordinary differential equation. Comput. appl. Math. (1991) · Zbl 0743.65065