Abstract
Three different finite difference schemes for solving the heat equation in one space dimension with boundary conditions containing integrals over the interior of the interval are considered. The schemes are based on the forward Euler, the backward Euler and the Crank-Nicolson methods. Error estimates are derived in maximum norm. Results from a numerical experiment are presented.
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Ekolin, G. Finite difference methods for a nonlocal boundary value problem for the heat equation. BIT 31, 245–261 (1991). https://doi.org/10.1007/BF01931285
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DOI: https://doi.org/10.1007/BF01931285