Algorithms for Numerical Solving of 2D Anomalous Diffusion Problems

Abstract

Fractional analog of the reaction diffusion equation is used to model the subdiffusion process. Diffusion equation with fractional Riemann–Liouville operator is analyzed in this paper. We offer finite-difference methods that can be used to solve the initial-boundary value problems for some time-fractional order differential equations. Stability and convergence theorems are proved.

Keywords:

• subdiffusion process
• fractional order differential equation

AMS Subject Classification:

• 65N06
• 65N12
• 65Z05
• 92C10
• 92C05