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

Chen, An

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.

PARTIAL differential equations; FRACTIONAL differential equations; FINITE element method; RIESZ spaces; NUMERICAL analysis; GALERKIN methods

Computer Modeling in Engineering & Sciences (CMES), 2020, Vol 123, Issue 3, p917

1526-1492

Academic Journal

10.32604/cmes.2020.09224