On the stability of fully-explicit finite-difference scheme for two-dimensional parabolic equation with nonlocal conditions

Abstract

We construct and analyse a fully-explicit finite-difference scheme for a two-dimensional parabolic equation with nonlocal integral conditions. The main attention is paid to the stability of the scheme. We apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite-difference scheme and demonstrate that depending on the parameters of nonlocal conditions the proposed method can be stable or unstable. The results of numerical experiment with one test problem are also presented and they validate theoretical results.