Compact Finite Difference Approximations for Space Fractional Diffusion Equations

Abstract

Based on the weighted and shifted Grünwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the one and two dimensional space fractional diffusion equations. The detailed numerical stability and error analysis are theoretically performed. We theoretically prove and numerically verify that the provided numerical schemes have the convergent orders 3 in space and 2 in time.

19 pages, 2 figures

References in corpus (1)

• A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations

Cited by in corpus (18)

• A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations
• Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
• Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions
• High order schemes for the tempered fractional diffusion equations
• An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation
• WSLD operators II: the new fourth order difference approximations for space Riemann-Liouville derivative
• Numerical Approximations for Fractional Differential Equations
• A Series of High Order Quasi-Compact Schemes for Space Fractional Diffusion Equations Based on the Superconvergent Approximations for Fractional Derivatives
• Numerical algorithms for the forward and backward fractional Feynman-Kac equations
• High-order Compact Difference Schemes for the Modified Anomalous Subdiffusion Equation
• Multi-domain Spectral Collocation Method for Variable-Order Nonlinear Fractional Differential Equations
• Third order quasi-compact schemes for space tempered fractional diffusion equations
• Second-order LOD multigrid method for multidimensional Riesz fractional diffusion equation
• Positivity and Boundedness Preserving Schemes for Space-Time Fractional Predator-Prey Reaction-Diffusion Model
• High Order Finite Difference Methods on Non-uniform Meshes for Space Fractional Operators
• A general explicit form for higher order approximations for fractional derivatives and its consequences
• A conservative difference scheme with optimal pointwise error estimates for two-dimensional space fractional nonlinear Schrödinger equations
• A Fourth-Order Compact ADI Scheme for Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation