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 - <p style="text-align: justify;">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. &nbsp;</p>