A Weighted Average Finite Difference Method for the Fractional Convection-Diffusion Equation

Abstract EN

A weighted average finite difference method for solving the two-sided space-fractional convection-diffusion equation is given, which is an extension of the weighted average method for ordinary convection-diffusion equations.

Stability, consistency, and convergence of the new method are analyzed.

A simple and accurate stability criterion valid for this method, arbitrary weighted factor, and arbitrary fractional derivative is given.

Some numerical examples with known exact solutions are provided.