Open Access

ARTICLE

Crank-Nicolson ADI Galerkin Finite Element Methods for Two Classes of Riesz Space Fractional Partial Differential Equations

An Chen^{1, *}

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.

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