Volume 6, Issue 1
Numerical Analysis for a Nonlocal Allen-Cahn Equation

Int. J. Numer. Anal. Mod., 6 (2009), pp. 33-49.

Published online: 2009-06

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• 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.

• Keywords

Finite difference scheme, long range interaction.

• AMS Subject Headings

35K57, 34A34, 65L12, 65N06

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-33, author = {P. W. and Bates and and 21016 and and P. W. Bates and S. and Brown and and 21017 and and S. Brown and J. and Han and and 21018 and and J. Han}, title = {Numerical Analysis for a Nonlocal Allen-Cahn Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/755.html} }
TY - JOUR T1 - Numerical Analysis for a Nonlocal Allen-Cahn Equation AU - Bates , P. W. AU - Brown , S. AU - Han , J. JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 33 EP - 49 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/755.html KW - Finite difference scheme, long range interaction. AB -

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.

P. W. Bates, S. Brown & J. Han. (1970). Numerical Analysis for a Nonlocal Allen-Cahn Equation. International Journal of Numerical Analysis and Modeling. 6 (1). 33-49. doi:
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