Abstract
In this article, 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.
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