Volume 16, Issue 5
Long Time Asymptotic Behavior of Solution of Difference Scheme for a Semilinear Parabolic Equation
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J. Comp. Math., 16 (1998), pp. 395-402

Published online: 1998-10

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• Abstract

In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as $t\rightarrow\infty$. For the discrete solution of nonlinear parabolic problem, we get its long time asymptotic behavior which is similar to that of the continuous solution. For simplicity, we consider one-dimensional problem.

• Keywords

Asymptotic behavior implicit difference scheme semilinear parabolic equation

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@Article{JCM-16-395, author = {}, title = {Long Time Asymptotic Behavior of Solution of Difference Scheme for a Semilinear Parabolic Equation}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {5}, pages = {395--402}, abstract = { In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as $t\rightarrow\infty$. For the discrete solution of nonlinear parabolic problem, we get its long time asymptotic behavior which is similar to that of the continuous solution. For simplicity, we consider one-dimensional problem. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9170.html} }
TY - JOUR T1 - Long Time Asymptotic Behavior of Solution of Difference Scheme for a Semilinear Parabolic Equation JO - Journal of Computational Mathematics VL - 5 SP - 395 EP - 402 PY - 1998 DA - 1998/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9170.html KW - Asymptotic behavior KW - implicit difference scheme KW - semilinear parabolic equation AB - In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as $t\rightarrow\infty$. For the discrete solution of nonlinear parabolic problem, we get its long time asymptotic behavior which is similar to that of the continuous solution. For simplicity, we consider one-dimensional problem.
Hui Feng & Long-jun Shen. (1970). Long Time Asymptotic Behavior of Solution of Difference Scheme for a Semilinear Parabolic Equation. Journal of Computational Mathematics. 16 (5). 395-402. doi:
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