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 - <p style="text-align: justify;">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>