Crank–Nicolson alternative direction implicit method for space-fractional diffusion equations with nonseparable coefficients

Xue Lei Lin, Kwok Po NG*, Hai Wei Sun

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

In this paper, we study the Crank–Nicolson alternative direction implicit (ADI) method for two-dimensional Riesz space-fractional diffusion equations with nonseparable coefficients. Existing ADI methods are only shown to be unconditional stable when coefficients are some special separable functions. The main contribution of this paper is to show under mild assumptions the unconditional stability of the proposed Crank–Nicolson ADI method in discrete 2 norm and the consistency of cross perturbation terms arising from the Crank–Nicolson ADI method. Also, we demonstrate that several consistent spatial discretization schemes satisfy the required assumptions. Numerical results are presented to examine the accuracy and the efficiency of the proposed ADI methods.

Original languageEnglish
Pages (from-to)997-1019
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume57
Issue number3
DOIs
Publication statusPublished - 2019

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Crank–Nicolson ADI methods
  • Nonseparable variable coefficients
  • Space-fractional diffusion equations
  • Unconditional stability analysis

Fingerprint

Dive into the research topics of 'Crank–Nicolson alternative direction implicit method for space-fractional diffusion equations with nonseparable coefficients'. Together they form a unique fingerprint.

Cite this