On the NBVP for Semilinear Hyperbolic Equations

Necmettin Aggez, Gulay Yucel

This paper is concerned with establishing the solvability of the nonlocal boundary value problem for the semilinear hyperbolic equation in a Hilbert space. For the approximate solution of this problem, the first order of accuracy difference scheme is presented. Under some assumptions, the convergence estimate for the solution of this difference scheme is obtained. Moreover, these results are supported by a numerical example.