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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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COPYRIGHT: © Global Science Press

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@Article{JCM-19-449, author = {Wan , Zheng-Su and , Zhi-Zhong Sun}, 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 AU - Wan , Zheng-Su AU - , Zhi-Zhong Sun 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, Nonlocal, $L_\infty$ convergence, 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.

Wan , Zheng-Su and , Zhi-Zhong Sun. (2001). 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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