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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.

MSC:

65Z05 Applications to the sciences
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
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[1] Dodd, R. K.; Eibeck, J. C.; Gibbon, J. D.; Morris, H. C., Solitons and Nonlinear Wave Equations (1982), Academic · 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), in press. · Zbl 0743.65065
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