On the NBVP for Semilinear Hyperbolic Equations

Abstract

A nonlocal boundary value problem for the semilinear hyperbolic equation in a Hilbert space is considered. The uniqueness of the solution of this problem is established. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. The convergence estimates for the solution of these difference schemes are obtained. To validate the main results, these difference schemes applied to the one dimensional semilinear hyperbolic problem.