Numerical analysis for a nonlocal Allen-Cahn equation
Peter W. Bates 1, Sarah Brown 2, Jianlong Han 21 Department of Mathematics, Michigan State University East Lansing, MI 48824, USA.
2 Department of Mathematics, Southern Utah University, Cedar City, UT 84720, USA.
Received by the editors May 1, 2007 and, in revised form, December 13, 2007.
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^\infinity norm.
AMS subject classifications: 35K57, 34A34, 65L12, 65N06
Key words: Finite difference scheme, long range interaction.
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