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Finite difference solution of a nonlinear Klein-Gordon equation with an external source. (English) Zbl 1215.65138

This paper is concerned with numerical approximation of solutions to the nonlinear one dimensional Klein-Gordon equation with an external source. The numerical approach relies on finite difference scheme on a four-point stencil without any requirement of additional iterations between levels. In this setting the authors prove that the finite difference scheme is convergent with the rate \(O(h^2)\) provided the exact solution belongs to \(W^2_2\) Sobolev space. Some numerical experiments are performed to support the theoretical findings.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
35Q40 PDEs in connection with quantum mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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