Second order WSGD operators II: A new family of difference schemes for space fractional advection diffusion equation

Abstract

The second order weighted and shifted Grünwald difference (WSGD) operators are developed in [Tian et al., arXiv:1201.5949] to solve space fractional partial differential equations. Along this direction, we further design a new family of second order WSGD operators; by properly choosing the weighted parameters, they can be effectively used to discretize space (Riemann-Liouville) fractional derivatives. Based on the new second order WSGD operators, we derive a family of difference schemes for the space fractional advection diffusion equation. By von Neumann stability analysis, it is proved that the obtained schemes are unconditionally stable. Finally, extensive numerical experiments are performed to demonstrate the performance of the schemes and confirm the convergent orders.

arXiv comment21 pages, 5 figures

References in corpus (3)

• A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations
• Second order finite difference approximations for the two-dimensional time-space Caputo-Riesz fractional diffusion equation
• Higher order Grünwald approximations of fractional derivatives and fractional powers of operators

Cited by in corpus (4)

• A Series of High Order Quasi-Compact Schemes for Space Fractional Diffusion Equations Based on the Superconvergent Approximations for Fractional Derivatives
• 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 collocation method of lines for two-sided space-fractional advection-diffusion equations with variable coefficients