Volume 19, Issue 5
On the L_infty Convergence and the Extrapolation Method of a Difference Scheme for Nonlocal Parabolic Equation with Natural Boundary Conditions

Zheng Su Wan & Zhi Zhong Sun

J. Comp. Math., 19 (2001), pp. 449-458

Published online: 2001-10

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  • 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.

  • Keywords

Parabolic Nonlocal L_infty convergence Extrapolation method

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@Article{JCM-19-449, author = {}, title = {On the L_infty Convergence and the Extrapolation Method of a Difference Scheme for Nonlocal Parabolic Equation with Natural Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {5}, pages = {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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8997.html} }
TY - JOUR T1 - On the L_infty Convergence and the Extrapolation Method of a Difference Scheme for Nonlocal Parabolic Equation with Natural Boundary Conditions JO - Journal of Computational Mathematics VL - 5 SP - 449 EP - 458 PY - 2001 DA - 2001/10 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8997.html KW - Parabolic KW - Nonlocal KW - L_infty convergence KW - Extrapolation method AB - 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.
Zheng Su Wan & Zhi Zhong Sun. (1970). On the L_infty Convergence and the Extrapolation Method of a Difference Scheme for Nonlocal Parabolic Equation with Natural Boundary Conditions. Journal of Computational Mathematics. 19 (5). 449-458. doi:
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