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Article: Crank–Nicolson alternative direction implicit method for space-fractional diffusion equations with nonseparable coefficients
Title | Crank–Nicolson alternative direction implicit method for space-fractional diffusion equations with nonseparable coefficients |
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Authors | |
Keywords | Nonseparable variable coefficients Space-fractional diffusion equations Unconditional stability analysis Crank–Nicolson ADI methods |
Issue Date | 2019 |
Citation | SIAM Journal on Numerical Analysis, 2019, v. 57, n. 3, p. 997-1019 How to Cite? |
Abstract | © 2019 Society for Industrial and Applied Mathematics 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. |
Persistent Identifier | http://hdl.handle.net/10722/276525 |
ISSN | 2023 Impact Factor: 2.8 2023 SCImago Journal Rankings: 2.163 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lin, Xue Lei | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Sun, Hai Wei | - |
dc.date.accessioned | 2019-09-18T08:33:52Z | - |
dc.date.available | 2019-09-18T08:33:52Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | SIAM Journal on Numerical Analysis, 2019, v. 57, n. 3, p. 997-1019 | - |
dc.identifier.issn | 0036-1429 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276525 | - |
dc.description.abstract | © 2019 Society for Industrial and Applied Mathematics 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. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Numerical Analysis | - |
dc.subject | Nonseparable variable coefficients | - |
dc.subject | Space-fractional diffusion equations | - |
dc.subject | Unconditional stability analysis | - |
dc.subject | Crank–Nicolson ADI methods | - |
dc.title | Crank–Nicolson alternative direction implicit method for space-fractional diffusion equations with nonseparable coefficients | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/18M1195693 | - |
dc.identifier.scopus | eid_2-s2.0-85067054052 | - |
dc.identifier.volume | 57 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 997 | - |
dc.identifier.epage | 1019 | - |
dc.identifier.isi | WOS:000473085400002 | - |
dc.identifier.issnl | 0036-1429 | - |