Matrix time-extrapolation algorithm for solving semilinear parabolic problems

详细信息    查看全文

• 作者：Xiangqi Wang ^{xiangqi.wang@forxmail.com" class="auth_mail" title="E-mail the corresponding author} ; Chuanmiao Chen ; ^{cmchen@hunnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Crank&ndash ; Nicolson ; Finite element ; Matrix time-extrapolation ; Semilinear parabolic
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：64
• 期：Complete
• 页码：162-169
• 全文大小：1088 K

文摘

In this letter, we propose a fast matrix time-extrapolation algorithm to solve semilinear parabolic problems of Crank–Nicolson-based finite element scheme, which employs exact matrix values computed by integral at time levels m$m$, m+p$m+p$, m+2p$m+2p$ to construct quadratic interpolation so that we can estimate matrix values at levels m+2p+1,m+2p+2,…,m+3p−1$m+2p+1,m+2p+2,\dots ,m+3p-1$, then the matrix value is recalculated at the level m+3p$m+3p$. This process is performed iteratively, and finally, the calculation for matrices decreases to 1∕p$1∕p$. The error estimate of this algorithm is proven, and numerical examples are established to support this theory.