Stability and convergence of finite difference method for two-sided space-fractional diffusion equations
In this paper, we study and analyse Crank–Nicolson (CN) temporal discretization with certain spatial difference schemes for one- and two-dimensional two-sided space-fractional diffusion equations (TSFDEs) with variable diffusion coefficients. The stability and convergence of the resulting discretiza...
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| Published in | Computers & mathematics with applications (1987) Vol. 89; pp. 78 - 86 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.05.2021
Elsevier BV |
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| ISSN | 0898-1221 1873-7668 |
| DOI | 10.1016/j.camwa.2021.02.018 |
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| Abstract | In this paper, we study and analyse Crank–Nicolson (CN) temporal discretization with certain spatial difference schemes for one- and two-dimensional two-sided space-fractional diffusion equations (TSFDEs) with variable diffusion coefficients. The stability and convergence of the resulting discretization linear systems for TSFDEs with variable diffusion coefficients are proven by a new technique. That is, under mild assumption, the scheme is unconditionally stable and convergent with O(τ2+hl)(l≥1), where τ and h denote the temporal and spatial mesh steps, respectively. Further, we show that several numerical schemes with lth order accuracy from the literature satisfy the required assumption. Numerical examples are implemented to illustrate our theoretical analyses. |
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| AbstractList | In this paper, we study and analyse Crank–Nicolson (CN) temporal discretization with certain spatial difference schemes for one- and two-dimensional two-sided space-fractional diffusion equations (TSFDEs) with variable diffusion coefficients. The stability and convergence of the resulting discretization linear systems for TSFDEs with variable diffusion coefficients are proven by a new technique. That is, under mild assumption, the scheme is unconditionally stable and convergent with O (τ2 + h1), where (l ≥ 1), τ and h denote the temporal and spatial mesh steps, respectively. Further, we show that several numerical schemes with lth order accuracy from the literature satisfy the required assumption. Numerical examples are implemented to illustrate our theoretical analyses. In this paper, we study and analyse Crank–Nicolson (CN) temporal discretization with certain spatial difference schemes for one- and two-dimensional two-sided space-fractional diffusion equations (TSFDEs) with variable diffusion coefficients. The stability and convergence of the resulting discretization linear systems for TSFDEs with variable diffusion coefficients are proven by a new technique. That is, under mild assumption, the scheme is unconditionally stable and convergent with O(τ2+hl)(l≥1), where τ and h denote the temporal and spatial mesh steps, respectively. Further, we show that several numerical schemes with lth order accuracy from the literature satisfy the required assumption. Numerical examples are implemented to illustrate our theoretical analyses. |
| Author | She, Zi-Hang Liu, Xuan Qu, Hai-Dong |
| Author_xml | – sequence: 1 givenname: Zi-Hang surname: She fullname: She, Zi-Hang – sequence: 2 givenname: Hai-Dong surname: Qu fullname: Qu, Hai-Dong – sequence: 3 givenname: Xuan surname: Liu fullname: Liu, Xuan email: 0950@hstc.edu.cn |
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| Cites_doi | 10.1090/S0025-5718-2015-02917-2 10.1016/j.camwa.2017.02.040 10.1137/13093933X 10.1007/s10915-012-9661-0 10.1063/1.1416180 10.1016/j.cam.2019.06.008 10.1007/s10444-016-9476-x 10.1016/j.apnum.2005.02.008 10.1029/2000WR900031 10.1137/0517050 10.1080/00207160.2017.1401707 10.1016/j.cam.2011.01.011 10.1016/j.apnum.2018.12.002 10.1137/080714130 10.1007/s42967-019-00050-9 10.1016/j.apnum.2014.11.007 10.1016/j.jcp.2014.10.053 10.1109/TIP.2007.904971 10.1029/2000WR900032 10.1137/130934192 10.1137/130933447 10.3934/naco.2014.4.317 10.1016/S0370-1573(00)00070-3 10.1007/s10915-017-0417-8 10.1007/s10915-017-0581-x 10.1007/s10444-015-9430-3 10.1007/s10915-016-0317-3 10.1137/16M1076083 |
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| Keywords | Variable diffusion coefficients Stability and convergence Two-sided space-fractional diffusion equation |
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| References | Hairer, Wanner (b26) 1996 Laub (b27) 2005 Zhou, Tian, Deng (b17) 2013; 56 Sousa, Li (b12) 2015; 90 Deng (b8) 2009; 47 Meerschaert, Tadjeran (b11) 2006; 56 Chen, Wang, Ding, Lei (b4) 2017; 73 Metzler, Klafter (b5) 2000; 339 Jin, Lazarov, Pasciak, Zhou (b10) 2014; 52 Zeng, Mao, Karniadakis (b31) 2017; 39 Benson, Wheatcraft, Meerschaert (b2) 2000; 36 Zeng, Liu, Li, Burrage, Turner, Anh (b14) 2014; 52 Zhao, Deng (b28) 2016; 42 Chen, Deng (b20) 2014; 52 Lin, Lyu, Ng, Sun, Vong (b24) 2020; 2 Ding, Li (b16) 2017; 71 Carreras, Lynch, Zaslavsky (b1) 2001; 8 Bai, Feng (b7) 2007; 16 Vong, Lyu (b23) 2019; 137 Kopteva, Stynes (b29) 2017; 43 Jiang, Ma (b9) 2011; 235 Lubich (b19) 1986; 17 Quarteroni, Sacco, Saleri (b25) 2007 Abirami, Prakash, Thangavel (b6) 2018; 95 Lin, Ng, Sun (b22) 2018; 75 Hao, Sun, Cao (b18) 2015; 281 Tian, Zhou, Deng (b13) 2015; 84 Lin, Liu (b15) 2020; 363 Qu, Lei, Vong (b21) 2014; 4 Benson, Wheatcraft, Meerschaert (b3) 2000; 36 Hao, Cao (b30) 2017; 73 Quarteroni (10.1016/j.camwa.2021.02.018_b25) 2007 Sousa (10.1016/j.camwa.2021.02.018_b12) 2015; 90 Vong (10.1016/j.camwa.2021.02.018_b23) 2019; 137 Jiang (10.1016/j.camwa.2021.02.018_b9) 2011; 235 Zhou (10.1016/j.camwa.2021.02.018_b17) 2013; 56 Lin (10.1016/j.camwa.2021.02.018_b22) 2018; 75 Bai (10.1016/j.camwa.2021.02.018_b7) 2007; 16 Zhao (10.1016/j.camwa.2021.02.018_b28) 2016; 42 Metzler (10.1016/j.camwa.2021.02.018_b5) 2000; 339 Abirami (10.1016/j.camwa.2021.02.018_b6) 2018; 95 Lin (10.1016/j.camwa.2021.02.018_b15) 2020; 363 Qu (10.1016/j.camwa.2021.02.018_b21) 2014; 4 Jin (10.1016/j.camwa.2021.02.018_b10) 2014; 52 Deng (10.1016/j.camwa.2021.02.018_b8) 2009; 47 Meerschaert (10.1016/j.camwa.2021.02.018_b11) 2006; 56 Carreras (10.1016/j.camwa.2021.02.018_b1) 2001; 8 Lin (10.1016/j.camwa.2021.02.018_b24) 2020; 2 Zeng (10.1016/j.camwa.2021.02.018_b31) 2017; 39 Tian (10.1016/j.camwa.2021.02.018_b13) 2015; 84 Chen (10.1016/j.camwa.2021.02.018_b4) 2017; 73 Laub (10.1016/j.camwa.2021.02.018_b27) 2005 Hairer (10.1016/j.camwa.2021.02.018_b26) 1996 Benson (10.1016/j.camwa.2021.02.018_b2) 2000; 36 Hao (10.1016/j.camwa.2021.02.018_b18) 2015; 281 Chen (10.1016/j.camwa.2021.02.018_b20) 2014; 52 Benson (10.1016/j.camwa.2021.02.018_b3) 2000; 36 Lubich (10.1016/j.camwa.2021.02.018_b19) 1986; 17 Ding (10.1016/j.camwa.2021.02.018_b16) 2017; 71 Zeng (10.1016/j.camwa.2021.02.018_b14) 2014; 52 Kopteva (10.1016/j.camwa.2021.02.018_b29) 2017; 43 Hao (10.1016/j.camwa.2021.02.018_b30) 2017; 73 |
| References_xml | – volume: 39 start-page: A360 year: 2017 end-page: A383 ident: b31 article-title: A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities publication-title: SIAM J. Sci. Comput. – volume: 339 start-page: 1 year: 2000 end-page: 77 ident: b5 article-title: The random walk’s guide to anomalous diffusion: a fractional dynamics approach publication-title: Phys. Rep. – year: 2005 ident: b27 article-title: Matrix Analysis for Scientists and Engineers – volume: 71 start-page: 759 year: 2017 end-page: 784 ident: b16 article-title: High-order numerical algorithms for Riesz derivatives via constructing new generating functions publication-title: J. Sci. Comput. – volume: 52 start-page: 2599 year: 2014 end-page: 2622 ident: b14 article-title: A Crank-Nicolson ADI spectral method for a two-dimensional Riesz space fractional nonlinear reaction-diffusion equation publication-title: SIAM J. Numer. Anal. – volume: 95 start-page: 1222 year: 2018 end-page: 1239 ident: b6 article-title: Fractional diffusion equation-based image denoising model using CN–GL scheme publication-title: Int. J. Comput. Math. – volume: 363 start-page: 77 year: 2020 end-page: 91 ident: b15 article-title: The accuracy and stability of CN-WSGD schemes for space fractional diffusion equation publication-title: J. Comput. Appl. Math. – volume: 73 start-page: 1932 year: 2017 end-page: 1944 ident: b4 article-title: A fast precondtioned policy iteration method for solving the tempered fractional HJB equation governing American options valuation publication-title: Comput. Math. Appl. – year: 1996 ident: b26 article-title: Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems – volume: 42 start-page: 425 year: 2016 end-page: 468 ident: b28 article-title: High order finite difference methods on non-uniform meshes for space fractional operators publication-title: Adv. Comput. Math. – volume: 16 start-page: 2492 year: 2007 end-page: 2502 ident: b7 article-title: Fractional-order anisotropic diffusion for image denoising publication-title: IEEE Tran. Image Proc. – volume: 52 start-page: 2272 year: 2014 end-page: 2294 ident: b10 article-title: Error analysis of a finite element method for the space-fractional parabolic equation publication-title: SIAM J. Numer. Anal. – volume: 36 start-page: 1413 year: 2000 end-page: 1423 ident: b3 article-title: The fractional-order governing equation of Lévy motion publication-title: Water Resour. Res. – volume: 17 start-page: 704 year: 1986 end-page: 719 ident: b19 article-title: Discretized fractional calculus publication-title: SIAM J. Math. Anal. – volume: 47 start-page: 204 year: 2009 end-page: 226 ident: b8 article-title: Finite element method for the space and time fractional Fokker–Planck equation publication-title: SIAM J. Numer. Anal. – volume: 36 start-page: 1403 year: 2000 end-page: 1412 ident: b2 article-title: Application of a fractional advection-dispersion equation publication-title: Water Resour. Res. – volume: 75 start-page: 1102 year: 2018 end-page: 1127 ident: b22 article-title: Stability and convergence analysis of finite difference schemes for time-dependent space-fractional diffusion equations with variable diffusion coefficients publication-title: J. Sci. Comput. – year: 2007 ident: b25 article-title: Numerical Mathematics – volume: 235 start-page: 3285 year: 2011 end-page: 3290 ident: b9 article-title: High-order finite element methods for time-fractional partial differential equations publication-title: J. Comput. Appl. Math. – volume: 56 start-page: 80 year: 2006 end-page: 90 ident: b11 article-title: Finite difference approximations for two-sided space-fractional partial differential equations publication-title: Appl. Numer. Math. – volume: 56 start-page: 45 year: 2013 end-page: 66 ident: b17 article-title: Quasi-compact finite difference schemes for space fractional diffusion equations publication-title: J. Sci. Comput. – volume: 43 start-page: 77 year: 2017 end-page: 99 ident: b29 article-title: Analysis and numerical solution of a Riemann–Liouville fractional derivative two-point boundary value problem publication-title: Adv. Comput. Math. – volume: 52 start-page: 1418 year: 2014 end-page: 1438 ident: b20 article-title: Fourth order accurate scheme for the space fractional diffusion equations publication-title: SIAM J. Numer. Anal. – volume: 73 start-page: 395 year: 2017 end-page: 415 ident: b30 article-title: An improved algorithm based on finite difference schemes for fractional boundary value problems with nonsmooth solution publication-title: J. Sci. Comput. – volume: 137 start-page: 34 year: 2019 end-page: 48 ident: b23 article-title: On a second order scheme for space fractional diffusion equations with variable coefficients publication-title: Appl. Numer. Math. – volume: 281 start-page: 787 year: 2015 end-page: 805 ident: b18 article-title: A fourth-order approximation of fractional derivatives with its applications publication-title: J. Comput. Phys. – volume: 90 start-page: 22 year: 2015 end-page: 37 ident: b12 article-title: A weighted finite difference method for the fractional diffusion equation based on the Riemann–Liouville derivative publication-title: Appl. Numer. Math. – volume: 8 start-page: 5096 year: 2001 end-page: 5103 ident: b1 article-title: Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model publication-title: Phys. Plasmas – volume: 2 start-page: 215 year: 2020 end-page: 239 ident: b24 article-title: An efficient second-order convergent scheme for one-sided space fractional diffusion equations with variable coefficients publication-title: Commun. Appl. Math. Comput. – volume: 84 start-page: 1703 year: 2015 end-page: 1727 ident: b13 article-title: A class of second order difference approximations for solving space fractional diffusion equations publication-title: Math. Comp. – volume: 4 start-page: 317 year: 2014 end-page: 325 ident: b21 article-title: A note on the stability of a second order finite difference scheme for space fractional diffusion equations publication-title: Numer. Algebra Control Optim. – volume: 84 start-page: 1703 issue: 294 year: 2015 ident: 10.1016/j.camwa.2021.02.018_b13 article-title: A class of second order difference approximations for solving space fractional diffusion equations publication-title: Math. Comp. doi: 10.1090/S0025-5718-2015-02917-2 – volume: 73 start-page: 1932 issue: 9 year: 2017 ident: 10.1016/j.camwa.2021.02.018_b4 article-title: A fast precondtioned policy iteration method for solving the tempered fractional HJB equation governing American options valuation publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2017.02.040 – volume: 52 start-page: 2272 issue: 5 year: 2014 ident: 10.1016/j.camwa.2021.02.018_b10 article-title: Error analysis of a finite element method for the space-fractional parabolic equation publication-title: SIAM J. Numer. Anal. doi: 10.1137/13093933X – volume: 56 start-page: 45 issue: 1 year: 2013 ident: 10.1016/j.camwa.2021.02.018_b17 article-title: Quasi-compact finite difference schemes for space fractional diffusion equations publication-title: J. Sci. Comput. doi: 10.1007/s10915-012-9661-0 – volume: 8 start-page: 5096 issue: 12 year: 2001 ident: 10.1016/j.camwa.2021.02.018_b1 article-title: Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model publication-title: Phys. Plasmas doi: 10.1063/1.1416180 – volume: 363 start-page: 77 year: 2020 ident: 10.1016/j.camwa.2021.02.018_b15 article-title: The accuracy and stability of CN-WSGD schemes for space fractional diffusion equation publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2019.06.008 – volume: 43 start-page: 77 issue: 1 year: 2017 ident: 10.1016/j.camwa.2021.02.018_b29 article-title: Analysis and numerical solution of a Riemann–Liouville fractional derivative two-point boundary value problem publication-title: Adv. Comput. Math. doi: 10.1007/s10444-016-9476-x – volume: 56 start-page: 80 issue: 1 year: 2006 ident: 10.1016/j.camwa.2021.02.018_b11 article-title: Finite difference approximations for two-sided space-fractional partial differential equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2005.02.008 – volume: 36 start-page: 1403 issue: 6 year: 2000 ident: 10.1016/j.camwa.2021.02.018_b2 article-title: Application of a fractional advection-dispersion equation publication-title: Water Resour. Res. doi: 10.1029/2000WR900031 – year: 2005 ident: 10.1016/j.camwa.2021.02.018_b27 – volume: 17 start-page: 704 issue: 3 year: 1986 ident: 10.1016/j.camwa.2021.02.018_b19 article-title: Discretized fractional calculus publication-title: SIAM J. Math. Anal. doi: 10.1137/0517050 – volume: 95 start-page: 1222 issue: 6–7 year: 2018 ident: 10.1016/j.camwa.2021.02.018_b6 article-title: Fractional diffusion equation-based image denoising model using CN–GL scheme publication-title: Int. J. Comput. Math. doi: 10.1080/00207160.2017.1401707 – volume: 235 start-page: 3285 issue: 11 year: 2011 ident: 10.1016/j.camwa.2021.02.018_b9 article-title: High-order finite element methods for time-fractional partial differential equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2011.01.011 – year: 1996 ident: 10.1016/j.camwa.2021.02.018_b26 – volume: 137 start-page: 34 year: 2019 ident: 10.1016/j.camwa.2021.02.018_b23 article-title: On a second order scheme for space fractional diffusion equations with variable coefficients publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2018.12.002 – volume: 47 start-page: 204 issue: 1 year: 2009 ident: 10.1016/j.camwa.2021.02.018_b8 article-title: Finite element method for the space and time fractional Fokker–Planck equation publication-title: SIAM J. Numer. Anal. doi: 10.1137/080714130 – volume: 2 start-page: 215 year: 2020 ident: 10.1016/j.camwa.2021.02.018_b24 article-title: An efficient second-order convergent scheme for one-sided space fractional diffusion equations with variable coefficients publication-title: Commun. Appl. Math. Comput. doi: 10.1007/s42967-019-00050-9 – volume: 90 start-page: 22 year: 2015 ident: 10.1016/j.camwa.2021.02.018_b12 article-title: A weighted finite difference method for the fractional diffusion equation based on the Riemann–Liouville derivative publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2014.11.007 – volume: 281 start-page: 787 year: 2015 ident: 10.1016/j.camwa.2021.02.018_b18 article-title: A fourth-order approximation of fractional derivatives with its applications publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2014.10.053 – volume: 16 start-page: 2492 issue: 10 year: 2007 ident: 10.1016/j.camwa.2021.02.018_b7 article-title: Fractional-order anisotropic diffusion for image denoising publication-title: IEEE Tran. Image Proc. doi: 10.1109/TIP.2007.904971 – year: 2007 ident: 10.1016/j.camwa.2021.02.018_b25 – volume: 36 start-page: 1413 issue: 6 year: 2000 ident: 10.1016/j.camwa.2021.02.018_b3 article-title: The fractional-order governing equation of Lévy motion publication-title: Water Resour. Res. doi: 10.1029/2000WR900032 – volume: 52 start-page: 2599 issue: 6 year: 2014 ident: 10.1016/j.camwa.2021.02.018_b14 article-title: A Crank-Nicolson ADI spectral method for a two-dimensional Riesz space fractional nonlinear reaction-diffusion equation publication-title: SIAM J. Numer. Anal. doi: 10.1137/130934192 – volume: 52 start-page: 1418 issue: 3 year: 2014 ident: 10.1016/j.camwa.2021.02.018_b20 article-title: Fourth order accurate scheme for the space fractional diffusion equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/130933447 – volume: 4 start-page: 317 issue: 4 year: 2014 ident: 10.1016/j.camwa.2021.02.018_b21 article-title: A note on the stability of a second order finite difference scheme for space fractional diffusion equations publication-title: Numer. Algebra Control Optim. doi: 10.3934/naco.2014.4.317 – volume: 339 start-page: 1 issue: 1 year: 2000 ident: 10.1016/j.camwa.2021.02.018_b5 article-title: The random walk’s guide to anomalous diffusion: a fractional dynamics approach publication-title: Phys. Rep. doi: 10.1016/S0370-1573(00)00070-3 – volume: 73 start-page: 395 issue: 1 year: 2017 ident: 10.1016/j.camwa.2021.02.018_b30 article-title: An improved algorithm based on finite difference schemes for fractional boundary value problems with nonsmooth solution publication-title: J. Sci. Comput. doi: 10.1007/s10915-017-0417-8 – volume: 75 start-page: 1102 issue: 2 year: 2018 ident: 10.1016/j.camwa.2021.02.018_b22 article-title: Stability and convergence analysis of finite difference schemes for time-dependent space-fractional diffusion equations with variable diffusion coefficients publication-title: J. Sci. Comput. doi: 10.1007/s10915-017-0581-x – volume: 42 start-page: 425 issue: 2 year: 2016 ident: 10.1016/j.camwa.2021.02.018_b28 article-title: High order finite difference methods on non-uniform meshes for space fractional operators publication-title: Adv. Comput. Math. doi: 10.1007/s10444-015-9430-3 – volume: 71 start-page: 759 issue: 2 year: 2017 ident: 10.1016/j.camwa.2021.02.018_b16 article-title: High-order numerical algorithms for Riesz derivatives via constructing new generating functions publication-title: J. Sci. Comput. doi: 10.1007/s10915-016-0317-3 – volume: 39 start-page: A360 issue: 1 year: 2017 ident: 10.1016/j.camwa.2021.02.018_b31 article-title: A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities publication-title: SIAM J. Sci. Comput. doi: 10.1137/16M1076083 |
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| Snippet | In this paper, we study and analyse Crank–Nicolson (CN) temporal discretization with certain spatial difference schemes for one- and two-dimensional two-sided... |
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| SubjectTerms | Convergence Diffusion Dimensional stability Discretization Finite difference method Linear systems Stability and convergence Two-sided space-fractional diffusion equation Variable diffusion coefficients |
| Title | Stability and convergence of finite difference method for two-sided space-fractional diffusion equations |
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