Finite Difference Schemes for the Variable Coefficients Single and Multi-Term Time-Fractional Diffusion Equations with Non-Smooth Solutions on Graded and Uniform Meshes
Year: 2019
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 845–866
Abstract
Finite difference scheme for the variable coefficients subdiffusion equations with non-smooth solutions is constructed and analyzed. The spatial derivative is discretized on a uniform mesh, and L1 approximation is used for the discretization of the fractional time derivative on a possibly graded mesh. Stability of the proposed scheme is given using the discrete energy method. The numerical scheme is O (N−min{2−α,rα}) accurate in time, where α (0 < α < 1) is the order of the fractional time derivative, r is an index of the mesh partition, and it is second order accurate in space. Extension to multi-term time-fractional problems with nonhomogeneous boundary conditions is also discussed, with the stability and error estimate proved both in the discrete l2-norm and the l∞-norm on the nonuniform temporal mesh. Numerical results are given for both the two-dimensional single and multi-term time-fractional equations.
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/nmtma.OA-2018-0046
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 845–866
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Fractional diffusion equation graded mesh multi-term variable coefficients low regularity stability and convergence analysis.
-
Global superconvergence analysis of nonconforming finite element method for time fractional reaction-diffusion problem with anisotropic data
Wei, Yabing | Lü, Shujuan | Wang, Fenling | Liu, F. | Zhao, YanminComputers & Mathematics with Applications, Vol. 119 (2022), Iss. P.159
https://doi.org/10.1016/j.camwa.2022.06.010 [Citations: 3] -
Mapped Legendre-spectral method for high-dimensional multi-term time-fractional diffusion-wave equation with non-smooth solution
Moussa, H. | Saker, M. A. | Zaky, M. A. | Babatin, M. | Ezz-Eldien, S. S.Computational and Applied Mathematics, Vol. 44 (2025), Iss. 4
https://doi.org/10.1007/s40314-025-03123-z [Citations: 1] -
A robust higher-order finite difference technique for a time-fractional singularly perturbed problem
Sahoo, Sanjay Ku | Gupta, Vikas | Dubey, ShrutiMathematics and Computers in Simulation, Vol. 215 (2024), Iss. P.43
https://doi.org/10.1016/j.matcom.2023.08.013 [Citations: 6] -
High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation
Su, Baojin | Jiang, ZiwenAdvances in Difference Equations, Vol. 2020 (2020), Iss. 1
https://doi.org/10.1186/s13662-020-03128-4 [Citations: 3] -
Analysis of a scheme which preserves the dissipation and positivity of Gibbs' energy for a nonlinear parabolic equation with variable diffusion
Serna-Reyes, Adán J. | Macías-Díaz, J.E. | Reguera-López, NuriaApplied Numerical Mathematics, Vol. 183 (2023), Iss. P.355
https://doi.org/10.1016/j.apnum.2022.09.015 [Citations: 0] -
Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients
Cui, Mingrong
Computational and Applied Mathematics, Vol. 40 (2021), Iss. 5
https://doi.org/10.1007/s40314-021-01551-1 [Citations: 5]