Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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 $\ell^2$ 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.

Keywords

nonseparable variable coefficients, Crank–Nicolson ADI methods, space-fractional diffusion equations, unconditional stability analysis

Publication Date

10-2019

Source Publication Title

Journal of Scientific Computing

Volume

81

Issue

1

Start Page

375

End Page

391

Publisher

Springer

DOI

10.1007/s10915-019-01020-2

Link to Publisher's Edition

https://doi.org/10.1007/s10915-019-01020-2

ISSN (print)

08857474

ISSN (electronic)

15737691

Included in

Mathematics Commons

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