Year: 2009
Author: P. W. Bates, S. Brown, J. Han
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 1 : pp. 33–49
Abstract
We propose a stable, convergent finite difference scheme to solve numerically a nonlocal Allen-Cahn equation which may model a variety of physical and biological phenomena involving long-range spatial interaction. We also prove that the scheme is uniquely solvable and the numerical solution will approach the true solution in the $L^∞$ norm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-IJNAM-755
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 1 : pp. 33–49
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Finite difference scheme long range interaction.