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: chena@glut.edu.cn.
(This article belongs to this Special Issue:Numerical Methods for Differential and Integral Equations)
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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
Fractional partial differential equations, Galerkin approximation, alternating direction implicit method, stability, convergence.