The compact and Crank-Nicolson ADI schemes for two-dimensional semilinear multidelay parabolic equations

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• 作者：Qifeng Zhang^a ; ^b ; ^{zhangqifeng0504@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Chengjian Zhang^b ; ^{cjzhang@mail.hust.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Li Wang^c ; ^{lwang46@buffalo.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Semilinear multidelay parabolic equations ; ADI schemes ; Unique solvability ; Convergence ; Stability
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：306
• 期：Complete
• 页码：217-230
• 全文大小：1931 K

文摘

This paper deals with numerical solutions of initial–boundary value problems of the two-dimensional semilinear multidelay parabolic equations. Two types of alternating direction implicit (ADI) schemes are suggested. The unique solvability, convergence and unconditional stability of the schemes are analyzed and hence the corresponding criteria are established. Especially, by using the discrete energy method, it is proven that the compact ADI scheme can attain second-order accuracy in time and fourth-order accuracy in space, and the Crank–Nicolson ADI scheme has second order accuracy in both time and space. Numerical experiments are performed to verify the efficiency and accuracy of the both schemes.