We consider compact difference schemes of approximation order $$4+2 $$ on a three-point spatial stencil for the Klein–Gordon equations with constant and variable coefficients. New compact schemes are proposed for… Click to show full abstract
We consider compact difference schemes of approximation order $$4+2 $$ on a three-point spatial stencil for the Klein–Gordon equations with constant and variable coefficients. New compact schemes are proposed for one type of second-order quasilinear hyperbolic equations. In the case of constant coefficients, we prove the strong stability of the difference solution under small perturbations of the initial conditions, the right-hand side, and the coefficients of the equation. A priori estimates are obtained for the stability and convergence of the difference solution in strong mesh norms.
               
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