Numerical Analysis for a Nonlocal Allen-Cahn Equation

Numerical Analysis for a Nonlocal Allen-Cahn Equation

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.

Author Details

P. W. Bates

S. Brown

J. Han