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Article: Stability and Convergence Analysis of Finite Difference Schemes for Time-Dependent Space-Fractional Diffusion Equations with Variable Diffusion Coefficients
Title | Stability and Convergence Analysis of Finite Difference Schemes for Time-Dependent Space-Fractional Diffusion Equations with Variable Diffusion Coefficients |
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Authors | |
Keywords | Stability Convergence Variable diffusion coefficients Time-dependent space-fractional diffusion equation High-order finite difference schemes |
Issue Date | 2018 |
Citation | Journal of Scientific Computing, 2018, v. 75, n. 2, p. 1102-1127 How to Cite? |
Abstract | © 2017, Springer Science+Business Media, LLC. In this paper, we study and analyze Crank–Nicolson temporal discretization with high-order spatial difference schemes for time-dependent Riesz space-fractional diffusion equations with variable diffusion coefficients. To the best of our knowledge, there is no stability and convergence analysis for temporally 2nd-order or spatially jth-order (j≥ 3) difference schemes for such equations with variable coefficients. We prove under mild assumptions on diffusion coefficients and spatial discretization schemes that the resulting discretized systems are unconditionally stable and convergent with respect to discrete ℓ2-norm. We further show that several spatial difference schemes with jth-order (j= 1 , 2 , 3 , 4) truncation error satisfy the assumptions required in our analysis. As a result, we obtain a series of temporally 2nd-order and spatially jth-order (j= 1 , 2 , 3 , 4) unconditionally stable difference schemes for solving time-dependent Riesz space-fractional diffusion equations with variable coefficients. Numerical results are presented to illustrate our theoretical results. |
Persistent Identifier | http://hdl.handle.net/10722/276773 |
ISSN | 2023 Impact Factor: 2.8 2023 SCImago Journal Rankings: 1.248 |
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 | 2019-09-18T08:34:37Z | - |
dc.date.available | 2019-09-18T08:34:37Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Journal of Scientific Computing, 2018, v. 75, n. 2, p. 1102-1127 | - |
dc.identifier.issn | 0885-7474 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276773 | - |
dc.description.abstract | © 2017, Springer Science+Business Media, LLC. In this paper, we study and analyze Crank–Nicolson temporal discretization with high-order spatial difference schemes for time-dependent Riesz space-fractional diffusion equations with variable diffusion coefficients. To the best of our knowledge, there is no stability and convergence analysis for temporally 2nd-order or spatially jth-order (j≥ 3) difference schemes for such equations with variable coefficients. We prove under mild assumptions on diffusion coefficients and spatial discretization schemes that the resulting discretized systems are unconditionally stable and convergent with respect to discrete ℓ2-norm. We further show that several spatial difference schemes with jth-order (j= 1 , 2 , 3 , 4) truncation error satisfy the assumptions required in our analysis. As a result, we obtain a series of temporally 2nd-order and spatially jth-order (j= 1 , 2 , 3 , 4) unconditionally stable difference schemes for solving time-dependent Riesz space-fractional diffusion equations with variable coefficients. Numerical results are presented to illustrate our theoretical results. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Scientific Computing | - |
dc.subject | Stability | - |
dc.subject | Convergence | - |
dc.subject | Variable diffusion coefficients | - |
dc.subject | Time-dependent space-fractional diffusion equation | - |
dc.subject | High-order finite difference schemes | - |
dc.title | Stability and Convergence Analysis of Finite Difference Schemes for Time-Dependent Space-Fractional Diffusion Equations with Variable Diffusion Coefficients | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s10915-017-0581-x | - |
dc.identifier.scopus | eid_2-s2.0-85031924887 | - |
dc.identifier.volume | 75 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 1102 | - |
dc.identifier.epage | 1127 | - |
dc.identifier.isi | WOS:000428565100022 | - |
dc.identifier.issnl | 0885-7474 | - |