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Volume 21, Issue 5
Long Time Asymptotic Behavior of Solution of Implicit Difference Scheme for a Semi-Linear Parabolic Equation

Zhi-Zhong Sun & Long-Jun Shen

J. Comp. Math., 21 (2003), pp. 671-680.

Published online: 2003-10

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  • Abstract

In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation as $t$ tends to infinity. The long asymptotic behavior of its discrete solution is obtained which is analogous to that of its continuous solution. At last, a few results are also presented for Crank-Nicolson scheme.  

  • Keywords

Asymptotic behavior, Implicit difference scheme, Semi-linear parabolic equation, Convergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-671, author = {Sun , Zhi-Zhong and Shen , Long-Jun}, title = {Long Time Asymptotic Behavior of Solution of Implicit Difference Scheme for a Semi-Linear Parabolic Equation}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {5}, pages = {671--680}, abstract = {

In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation as $t$ tends to infinity. The long asymptotic behavior of its discrete solution is obtained which is analogous to that of its continuous solution. At last, a few results are also presented for Crank-Nicolson scheme.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10245.html} }
TY - JOUR T1 - Long Time Asymptotic Behavior of Solution of Implicit Difference Scheme for a Semi-Linear Parabolic Equation AU - Sun , Zhi-Zhong AU - Shen , Long-Jun JO - Journal of Computational Mathematics VL - 5 SP - 671 EP - 680 PY - 2003 DA - 2003/10 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10245.html KW - Asymptotic behavior, Implicit difference scheme, Semi-linear parabolic equation, Convergence. AB -

In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation as $t$ tends to infinity. The long asymptotic behavior of its discrete solution is obtained which is analogous to that of its continuous solution. At last, a few results are also presented for Crank-Nicolson scheme.  

Sun , Zhi-Zhong and Shen , Long-Jun. (2003). Long Time Asymptotic Behavior of Solution of Implicit Difference Scheme for a Semi-Linear Parabolic Equation. Journal of Computational Mathematics. 21 (5). 671-680. doi:
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