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ARTICLE
Crank-Nicolson ADI Galerkin Finite Element Methods for Two Classes of Riesz Space Fractional Partial Differential Equations
An Chen1, *
1 College of Science, Guilin University of Technology, Guilin, 541004, China.
* Corresponding Author: An Chen. Email: .
(This article belongs to the Special Issue: Numerical Methods for Differential and Integral Equations)
Computer Modeling in Engineering & Sciences 2020, 123(3), 917-939. https://doi.org/10.32604/cmes.2020.09224
Received 24 November 2019; Accepted 16 January 2020; Issue published 28 May 2020
Abstract
In this paper, two classes of Riesz space fractional partial differential equations
including space-fractional and space-time-fractional ones are considered. These two
models can be regarded as the generalization of the classical wave equation in two
space dimensions. Combining with the Crank-Nicolson method in temporal direction,
efficient alternating direction implicit Galerkin finite element methods for solving these two
fractional models are developed, respectively. The corresponding stability and convergence
analysis of the numerical methods are discussed. Numerical results are provided to verify
the theoretical analysis.
Keywords
Cite This Article
Chen, A. (2020). Crank-Nicolson ADI Galerkin Finite Element Methods for Two Classes of Riesz Space Fractional Partial Differential Equations.
CMES-Computer Modeling in Engineering & Sciences, 123(3), 917–939. https://doi.org/10.32604/cmes.2020.09224