@Article{JCM-33-1,
author = {V., Thomée and Vasudeva, Murthy, A.S.},
title = {Finite Difference Methods for the Heat Equation with a Nonlocal Boundary Condition},
journal = {Journal of Computational Mathematics},
year = {2015},
volume = {33},
number = {1},
pages = {17--32},
abstract = {<p style="text-align: justify;">We consider the numerical solution by finite difference methods of the heat equation in one space dimension, with a nonlocal integral boundary condition, resulting from the truncation to a finite interval of the problem on a semi-infinite interval. We first analyze the forward Euler method, and then the $θ$-method for $0 &lt; θ ≤ 1$, in both cases in maximum-norm, showing $O(h^2 + k)$ error bounds, where $h$ is the mesh-width and $k$ the time step. We then give an alternative analysis for the case $θ = 1/2$, the Crank-Nicolson method, using energy arguments, yielding a $O(h^2$ + $k^{3/2}$) error bound. Special attention is given the approximation of the boundary integral operator. Our results are illustrated by numerical examples.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1406-m4443},
url = {https://global-sci.com/article/84584/finite-difference-methods-for-the-heat-equation-with-a-nonlocal-boundary-condition}
}