Second order finite difference approximations for the two-dimensional time-space Caputo-Riesz fractional diffusion equation

Abstract

In this paper, we discuss the time-space Caputo-Riesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify that the implicit finite difference scheme is unconditionally stable (the explicit scheme is conditionally stable with the stability condition $\frac{{\tau }^{\gamma }}{(\Delta x{)}^{\alpha }}+\frac{{\tau }^{\gamma }}{(\Delta y{)}^{\beta }}<C$) and 2nd order convergent in space direction, and $(2-\gamma )$-th order convergent in time direction, where $\gamma \in (0,1]$.

27 pages

References in corpus (1)

• A second-order numerical method for two-dimensional two-sided space fractional convection diffusion equation

Cited by in corpus (9)

• WSLD operators: A class of fourth order difference approximations for space Riemann-Liouville derivative
• High order algorithms for the fractional substantial diffusion equation with truncated Lévy flights
• WSLD operators II: the new fourth order difference approximations for space Riemann-Liouville derivative
• Numerical Approximations for Fractional Differential Equations
• Numerical algorithms for the forward and backward fractional Feynman-Kac equations
• Second-order LOD multigrid method for multidimensional Riesz fractional diffusion equation
• Second order WSGD operators II: A new family of difference schemes for space fractional advection diffusion equation
• Correction of BDFk for fractional Feynman-Kac equation with Lévy flight
• General matrix transform method for the Riesz space fractional advection-dispersion equations