Close Search Advanced
Journals
Resources
About Us
Open Access

Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations

Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations
Preview
Add to basket

Year:    2014

Author:    Jincheng Ren, Zhi-Zhong Sun

East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 3 : pp. 242–266

Abstract

Some efficient numerical schemes are proposed for solving one-dimensional (1D) and two-dimensional (2D) multi-term time fractional sub-diffusion equations, combining the compact difference approach for the spatial discretisation and $L1$ approximation for the multi-term time Caputo fractional derivatives. The stability and convergence of these difference schemes are theoretically established. Several numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.181113.280514a

East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 3 : pp. 242–266

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Multi-term time fractional sub-diffusion equations compact/compact ADI difference scheme discrete energy method convergence.

Author Details

Jincheng Ren

Zhi-Zhong Sun

  1. Efficient numerical method for multi-term time-fractional diffusion equations with Caputo-Fabrizio derivatives

    Fan, Bin

    AIMS Mathematics, Vol. 9 (2024), Iss. 3 P.7293

    https://doi.org/10.3934/math.2024354 [Citations: 0]

  2. Stability and convergence of finite difference schemes for a class of time-fractional sub-diffusion equations based on certain superconvergence

    Gao, Guang-Hua | Sun, Hai-Wei | Sun, Zhi-Zhong

    Journal of Computational Physics, Vol. 280 (2015), Iss. P.510

    https://doi.org/10.1016/j.jcp.2014.09.033 [Citations: 95]

  3. A two-grid mixed finite element method for a nonlinear fourth-order reaction–diffusion problem with time-fractional derivative

    Liu, Yang | Du, Yanwei | Li, Hong | Li, Jichun | He, Siriguleng

    Computers & Mathematics with Applications, Vol. 70 (2015), Iss. 10 P.2474

    https://doi.org/10.1016/j.camwa.2015.09.012 [Citations: 125]

  4. Analysis of a fast element-free Galerkin method for the multi-term time-fractional diffusion equation

    Hu, Zesen | Li, Xiaolin

    Mathematics and Computers in Simulation, Vol. 223 (2024), Iss. P.677

    https://doi.org/10.1016/j.matcom.2024.05.008 [Citations: 1]

  5. The Unstructured Mesh Finite Element Method for the Two-Dimensional Multi-term Time–Space Fractional Diffusion-Wave Equation on an Irregular Convex Domain

    Fan, Wenping | Jiang, Xiaoyun | Liu, Fawang | Anh, Vo

    Journal of Scientific Computing, Vol. 77 (2018), Iss. 1 P.27

    https://doi.org/10.1007/s10915-018-0694-x [Citations: 27]

  6. Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation

    Zhao, Y.M. | Zhang, Y.D. | Liu, F. | Turner, I. | Shi, D.Y.

    Applied Mathematical Modelling, Vol. 40 (2016), Iss. 19-20 P.8810

    https://doi.org/10.1016/j.apm.2016.05.039 [Citations: 31]

  7. Efficient Numerical Solution of the Multi-Term Time Fractional Diffusion-Wave Equation

    Ren, Jincheng | Sun, Zhi-Zhong

    East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 1 P.1

    https://doi.org/10.4208/eajam.080714.031114a [Citations: 46]

  8. Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations

    Jin, Xiao-Qing | Lin, Fu-Rong | Zhao, Zhi

    Communications in Computational Physics, Vol. 18 (2015), Iss. 2 P.469

    https://doi.org/10.4208/cicp.120314.230115a [Citations: 44]

  9. A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation

    Lyu, Pin | Vong, Seakweng | Wang, Zhibo

    East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 4 P.752

    https://doi.org/10.4208/eajam.181016.300517e [Citations: 2]

  10. An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation

    Qiao, Leijie | Wang, Zhibo | Xu, Da

    Applied Numerical Mathematics, Vol. 151 (2020), Iss. P.199

    https://doi.org/10.1016/j.apnum.2020.01.003 [Citations: 44]

  11. High Spatial Accuracy Analysis of Linear Triangular Finite Element for Distributed Order Diffusion Equations

    He, Lin | Ren, Jincheng

    Taiwanese Journal of Mathematics, Vol. 24 (2020), Iss. 3

    https://doi.org/10.11650/tjm/190803 [Citations: 1]

  12. Orthogonal spline collocation scheme for multiterm fractional convection‐diffusion equation with variable coefficients

    Yang, Xuehua | Zhang, Haixiang | Xu, Da

    Numerical Methods for Partial Differential Equations, Vol. 34 (2018), Iss. 2 P.555

    https://doi.org/10.1002/num.22213 [Citations: 3]

  13. A weak Galerkin finite element method on temporal graded meshes for the multi-term time fractional diffusion equations

    Toprakseven, Şuayip

    Computers & Mathematics with Applications, Vol. 128 (2022), Iss. P.108

    https://doi.org/10.1016/j.camwa.2022.10.012 [Citations: 11]

  14. Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations

    Gao, Guang-hua | Sun, Zhi-zhong

    Journal of Scientific Computing, Vol. 66 (2016), Iss. 3 P.1281

    https://doi.org/10.1007/s10915-015-0064-x [Citations: 59]

  15. Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations

    Zhao, Yanmin | Zhang, Yadong | Liu, F. | Turner, I. | Tang, Yifa | Anh, V.

    Computers & Mathematics with Applications, Vol. 73 (2017), Iss. 6 P.1087

    https://doi.org/10.1016/j.camwa.2016.05.005 [Citations: 44]

  16. A Legendre spectral quadrature tau method for the multi-term time-fractional diffusion equations

    Zaky, Mahmoud A.

    Computational and Applied Mathematics, Vol. 37 (2018), Iss. 3 P.3525

    https://doi.org/10.1007/s40314-017-0530-1 [Citations: 58]

  17. Analysis of BDF2 finite difference method for fourth-order integro-differential equation

    Liu, Yanling | Yang, Xuehua | Zhang, Haixiang | Liu, Yuan

    Computational and Applied Mathematics, Vol. 40 (2021), Iss. 2

    https://doi.org/10.1007/s40314-021-01449-y [Citations: 3]

  18. Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

    Zeng, Fanhai | Zhang, Zhongqiang | Karniadakis, George Em

    Computer Methods in Applied Mechanics and Engineering, Vol. 327 (2017), Iss. P.478

    https://doi.org/10.1016/j.cma.2017.08.029 [Citations: 103]

  19. Design and analysis of a computational procedure for a class of time fractional multi-term diffusion problem

    Kanth, A. S. V. Ravi | Deepika, S.

    Soft Computing, Vol. 27 (2023), Iss. 3 P.1241

    https://doi.org/10.1007/s00500-022-07717-1 [Citations: 0]

  20. Discrete singular convolution for fourth-order multi-term time fractional equation

    Liu, Xingguo | Yang, Xuehua | Zhang, Haixiang | Liu, Yanling

    Tbilisi Mathematical Journal, Vol. 14 (2021), Iss. 2

    https://doi.org/10.32513/tmj/19322008118 [Citations: 0]

  21. A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation

    Lyu, Pin | Liang, Yuxiang | Wang, Zhibo

    Applied Numerical Mathematics, Vol. 151 (2020), Iss. P.448

    https://doi.org/10.1016/j.apnum.2019.11.012 [Citations: 40]

  22. High‐order compact finite difference method for the multi‐term time fractional mixed diffusion and diffusion‐wave equation

    Yu, Bo

    Mathematical Methods in the Applied Sciences, Vol. 44 (2021), Iss. 8 P.6526

    https://doi.org/10.1002/mma.7207 [Citations: 4]

  23. High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

    Su, Baojin | Jiang, Ziwen

    Advances in Difference Equations, Vol. 2020 (2020), Iss. 1

    https://doi.org/10.1186/s13662-020-03128-4 [Citations: 2]

  24. Computational Study of Multiterm Time‐Fractional Differential Equation Using Cubic B‐Spline Finite Element Method

    Arifeen, Shams Ul | Haq, Sirajul | Golkarmanesh, Farhan | Munoz-Pacheco, Jesus M.

    Complexity, Vol. 2022 (2022), Iss. 1

    https://doi.org/10.1155/2022/3160725 [Citations: 1]

  25. A compact exponential difference method for multi-term time-fractional convection-reaction-diffusion problems with non-smooth solutions

    Wang, Yuan-Ming | Wen, Xin

    Applied Mathematics and Computation, Vol. 381 (2020), Iss. P.125316

    https://doi.org/10.1016/j.amc.2020.125316 [Citations: 2]

  26. Superconvergence of FEM for Distributed Order Time Fractional Variable Coefficient Diffusion Equations

    Yang, Yanhua | Ren, Jincheng

    Taiwanese Journal of Mathematics, Vol. 22 (2018), Iss. 6

    https://doi.org/10.11650/tjm/180606 [Citations: 1]

  27. Simple positivity-preserving nonlinear finite volume scheme for subdiffusion equations on general non-conforming distorted meshes

    Yang, Xuehua | Zhang, Haixiang | Zhang, Qi | Yuan, Guangwei

    Nonlinear Dynamics, Vol. 108 (2022), Iss. 4 P.3859

    https://doi.org/10.1007/s11071-022-07399-2 [Citations: 33]

  28. A New Kind of Parallel Natural Difference Method for Multi-Term Time Fractional Diffusion Model

    Yang, Xiaozhong | Wu, Lifei

    Mathematics, Vol. 8 (2020), Iss. 4 P.596

    https://doi.org/10.3390/math8040596 [Citations: 9]

  29. Galerkin approximation for multi-term time-fractional differential equations

    Arifeen, Shams Ul | Haq, Sirajul | Ali, Ihteram | Aldosary, Saud Fahad

    Ain Shams Engineering Journal, Vol. 15 (2024), Iss. 7 P.102806

    https://doi.org/10.1016/j.asej.2024.102806 [Citations: 2]

  30. Finite difference/finite element method for a novel 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains

    Feng, Libo | Liu, Fawang | Turner, Ian

    Communications in Nonlinear Science and Numerical Simulation, Vol. 70 (2019), Iss. P.354

    https://doi.org/10.1016/j.cnsns.2018.10.016 [Citations: 66]

  31. Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations

    Wei, Ya-bing | Zhao, Yan-min | Shi, Zheng-guang | Wang, Fen-ling | Tang, Yi-fa

    Acta Mathematicae Applicatae Sinica, English Series, Vol. 34 (2018), Iss. 4 P.828

    https://doi.org/10.1007/s10255-018-0795-1 [Citations: 5]

  32. The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for Solving the Time Multi-term and Distributed-Order Fractional Sub-diffusion Equations

    Gao, Guang-hua | Alikhanov, Anatoly A. | Sun, Zhi-zhong

    Journal of Scientific Computing, Vol. 73 (2017), Iss. 1 P.93

    https://doi.org/10.1007/s10915-017-0407-x [Citations: 88]