Difference Schemes for the Semilinear Integral-Differential Equation of the Hyperbolic Type

Abstract

In this paper, the initial-value problem for integral-differential equation of the hyperbolic type in a Hilbert space H is considered. The unique solvability of this problem is established. The first order and the second order of accuracy difference schemes approximately solving this problem are presented. The convergence estimates for the solutions of these difference schemes are obtained. Theoretical results are supported by numerical example.