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

Qifeng Zhang, Chengjian Zhang, Li Wang

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)217-230
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume306
DOIs
StatePublished - Nov 1 2016
Externally publishedYes

Bibliographical note

Funding Information:
The authors are supported by NSFC (Grant No. 11571128, 11501514 ), Natural Science Foundation of Zhejiang Province (Grant No. LQ16A010007 ), Zhejiang Province Ministry of Education (Grant No. Y201533134 ) and School Initiation Funds in ZSTU (Grant No. 11432932611470) .

Publisher Copyright:
© 2016 Elsevier B.V. All rights reserved.

Keywords

  • ADI schemes
  • Convergence
  • Semilinear multidelay parabolic equations
  • Stability
  • Unique solvability

Fingerprint Dive into the research topics of 'The compact and Crank-Nicolson ADI schemes for two-dimensional semilinear multidelay parabolic equations'. Together they form a unique fingerprint.

Cite this