Explicit difference method for solving the two-dimensional two-sided fractional diffusion equation in the shifted grunwald estimate form

In this paper, we introduce and discuss an algorithm for the numerical solution of two-dimensional two-sided fractional diffusion equation. The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of the fractional order numerical method are described. Finally, numerical example is provided to show that the numerical method for solving this equation is an effective solution method.

کلیدواژه ها:

Fractional derivative ، Explicit euler method ، Fractional diffusion equation ، Stability ، Convergence