On stability analysis of finite difference schemes for some parabolic problems with nonlocal boundary conditions

Abstract

In this paper one dimensional parabolic and pseudo-parabolic equations with nonlocal boundary conditions are approximated by the implicit Euler finite difference scheme. For a parabolic problem the stability analysis is done in the weak H−1 type norm, which enables us to generalize results obtained in stronger norms. In the case of a pseudo-parabolic problem the stability analysis is done in the discrete analog of the norm. It is shown that a solution of the proposed finite discrete scheme satisfies stronger stability estimates than a discrete solution of the parabolic problem. Results of numerical experiments are presented.