CRANK-NICOLSON ADI METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NON-SEPARABLE COEFFICIENTS

UM > Faculty of Science and Technology > DEPARTMENT OF MATHEMATICS

Status	已發表Published
	CRANK-NICOLSON ADI METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NON-SEPARABLE COEFFICIENTS
	Lin, X.L.; Ng, M.K.; Sun, H. W.
	2019-05-01
Source Publication	SIAM Journal on Numerical Analysis
ISSN	0036-1429
Pages	997-1019
Abstract	In this paper, we study Crank-Nicolson ADI method for two-dimensional Riesz space-fractional diffusion equations with non-separable 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 l2 norm and the consistency of cross perturbation terms arising from 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 e fficiency of the proposed ADI methods.
Keyword	non-separable variable coe cients Crank-Nicolson ADI methods space-fractional di usion equations unconditional stability analysis
Language	英語English
The Source to Article	PB_Publication
PUB ID	43177
Document Type	Journal article
Collection	DEPARTMENT OF MATHEMATICS
Corresponding Author	Ng, M.K.
Recommended Citation GB/T 7714	Lin, X.L.,Ng, M.K.,Sun, H. W.. CRANK-NICOLSON ADI METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NON-SEPARABLE COEFFICIENTS[J]. SIAM Journal on Numerical Analysis, 2019, 997-1019.
APA	Lin, X.L.., Ng, M.K.., & Sun, H. W. (2019). CRANK-NICOLSON ADI METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NON-SEPARABLE COEFFICIENTS. SIAM Journal on Numerical Analysis, 997-1019.
MLA	Lin, X.L.,et al."CRANK-NICOLSON ADI METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NON-SEPARABLE COEFFICIENTS".SIAM Journal on Numerical Analysis (2019):997-1019.

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