NBVP for semilinear hyperbolic equations

摘要

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 order and the second order 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 are applied to the one dimensional semilinear hyperbolic problem.