On the $L_\infty$ Convergence and the Extrapolation Method of a Difference Scheme for Nonlocal Parabolic Equation with Natural Boundary Conditions
Year: 2001
Author: Zheng-Su Wan, Zhi-Zhong Sun
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 5 : pp. 449–458
Abstract
In paper [4] (J. Comput. Appl. Math.,76 (1996), 137-146), a difference scheme for a class of nonlocal parabolic equations with natural boundary conditions was derived by the method of reduction of order and the unique solvability and second order convergence in $L_2$-norm are proved. In this paper, we prove that the scheme is second order convergent in $L_\infty$ norm and then obtain fourth order accuracy approximation in $L_\infty$ norm by extrapolation method. At last, one numerical example is presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-8997
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 5 : pp. 449–458
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Parabolic Nonlocal $L_\infty$ convergence Extrapolation method.