A Compact Finite Difference Scheme for the Fourth-Order Time Multi-Term Fractional Sub-Diffusion Equations with the First Dirichlet Boundary Conditions
Year: 2021
Author: Guang-Hua Gao, Rui Tang, Qian Yang
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 1 : pp. 100–119
Abstract
In this paper, a finite difference scheme is established for solving the fourth-order time multi-term fractional sub-diffusion equations with the first Dirichlet boundary conditions. Using the method of order reduction, the original problem is equivalent to a lower-order system. Then the system is considered at some particular points, and the first Dirichlet boundary conditions are also specially handled, so that the global convergence of the presented difference scheme reaches $O(τ^2 + h^4)$, with $τ$ and $h$ the temporal and spatial step size, respectively. The energy method is used to give the theoretical analysis on the stability and convergence of the difference scheme, where some novel techniques have been applied due to the non-local property of fractional operators and the numerical treatment of the first Dirichlet boundary conditions. Numerical experiments further validate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-18623
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 1 : pp. 100–119
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Multi-term fractional sub-diffusion equations the first Dirichlet boundary conditions stability convergence.