Finite difference approach for variable order reaction–subdiffusion equations

Abstract

Abstract The fractional reaction–subdiffusion equation is one of the most famous subdiffusion equations. These equations are widely used in recent years to simulate many physical phenomena. In this paper, we consider a new version of such equations, namely the variable order linear and nonlinear reaction–subdiffusion equation. A numerical study is introduced using the weighted average methods for the variable order linear and nonlinear reaction–subdiffusion equations. A stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. The paper is ended with the results of numerical examples that support the theoretical analysis.

Keywords

• Weighted average finite difference approximations
• Variable order linear and nonlinear reaction–subdiffusion equation
• Stability analysis
• Numerical example