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

P. W. Bates, S. Brown & J. Han

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

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-33, author = {Bates , P. W.Brown , S. and Han , J.}, 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.

Bates , P. W.Brown , S. and Han , J.. (2009). Numerical Analysis for a Nonlocal Allen-Cahn Equation. International Journal of Numerical Analysis and Modeling. 6 (1). 33-49. doi:
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