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Int. J. Numer. Anal. Mod., 6 (2009), pp. 33-49. |
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Numerical analysis for a nonlocal Allen-Cahn equation Peter W. Bates 1, Sarah Brown 2, Jianlong Han 2 1 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. 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^\infinity norm. AMS subject classifications: 35K57, 34A34, 65L12, 65N06 Key words: Finite difference scheme, long range interaction. Email: bates@math.msu.edu, brown_s@suu.edu, han@suu.edu |