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An initial-boundary value problem of a nonlinear Klein-Gordon equation. (English) Zbl 0884.65091
A fully implicit and discrete energy conserving finite difference scheme for solving an initial-boundary value problem of the nonlinear Klein-Gordon equation is presented. A theoretical analysis is performed and it is demonstrated that the numerical scheme is especially attractive when long time solutions are sought.

65M06Finite difference methods (IVP of PDE)
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q40PDEs in connection with quantum mechanics
Full Text: DOI
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[6] Brezis, H.: Periodic solutions of nonlinear vibrating strings and duality principle. Bull. amer. Math. soc. (N.S.) 8, No. 3, 409-425 (1983)