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FD-method for solving the nonlinear Klein-Gordon equation. (English) Zbl 1277.65072

Ukr. Math. J. 64, No. 10, 1586-1609 (2013); translation from Ukr. Mat. Zh. 64, No. 10, 1394-1415 (2012).
The paper is interested in the solution of the Goursat problem for the nonlinear Klein-Gordon equation and a numerical-analytical method is proposed. Using general assumptions and provided that the mesh size is sufficiently small, the super-exponential convergence of this method are established. The obtained theoretical results are illustrated by a numerical example.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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