A high-order linearized compact finite difference method for nonlinear fractional mobile/immobile equations

Abstract

Based on the linearized techniques, a high-order linearized compact difference method is proposed for a class of nonlinear fractional mobile/immobile diffusion equations. In the proposed scheme, firstly a second e-order difference approximation is employed to approximate the time first derivative and Caputo time fractional derivative and then the spatial derivative is discretized by a fourth-order compact difference approximation. The convergence order of the resulting linearized compact difference method is $\mathcal{O}\left( {{\tau ^2} + {h^4}} \right)$ , where τ and h are the temporal and spatial steps, respectively. Numerical experiments are conducted to demonstrate the efficiency and accuracy of the proposed method.