An Implicit Difference Scheme for a Mixed Problem of Hyperbolic Type with Memory

In this article is proposed a method for numerically solving a mixed problem for a hyperbolic equation with memory. An implicit difference scheme is constructed as an effective means for solving complex multidimensional problems of mathematical physics. A condition is found for guaranteed stability of an implicit difference scheme for a mixed problem in the \(L^{2}\) -norm. The order of convergence for all variables of the presented difference scheme was calculated and confirmed by numerical experiment.