Abstract
We study a nonlocal boundary value problem for a parabolic equation in the multidimensional case. A locally one-dimensional difference scheme is constructed to solve this problem numerically. A priori estimates are derived by the method of energy inequalities in the differential and difference settings. The uniform convergence of the locally one-dimensional scheme is proved.
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Beshtokova, Z.V. Locally One-Dimensional Difference Scheme for a Nonlocal Boundary Value Problem for a Parabolic Equation in a Multidimensional Domain. Diff Equat 56, 354–368 (2020). https://doi.org/10.1134/S0012266120030088
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DOI: https://doi.org/10.1134/S0012266120030088