Finite difference solution of a nonlinear Klein-Gordon equation with an external source

Berikelashvili, G.; Jokhadze, O.; Kharibegashvili, S.; Midodashvili, B.

doi:10.1090/S0025-5718-2010-02416-0

Finite difference solution of a nonlinear Klein-Gordon equation with an external source
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by G. Berikelashvili, O. Jokhadze, S. Kharibegashvili and B. Midodashvili PDF

Math. Comp. 80 (2011), 847-862 Request permission

Abstract:

In this paper, we consider the Darboux problem for a (1+1)-dimensional cubic nonlinear Klein-Gordon equation with an external source. Stable finite difference scheme is constructed on a four-point stencil, which does not require additional iterations for passing from one level to another. It is proved, that the finite difference scheme converges with the rate $O(h^2)$, when the exact solution belongs to the Sobolev space $W_2^2$.

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