Compact difference schemes for multidimensional Klein–Gordon equations

Abstract. In this article, we consider a compact difference approximation of the schemes of order O(| h|4  +  τ2), h = (h1, h2, ..., hp) for the Klein–Gordon equations in the multidimensional case. In studying the stability of these difference schemes, the theory of operator-difference schemes by A. A. Samarskii is used, and the strong stability of difference schemes is proved with respect to a small perturbation of the initial conditions, the right-hand side and the coefficients of the equations. The theoretical results are confirmed by test numerical calculations.