gL1 Scheme for Solving a Class of Generalized Time-Fractional Diffusion Equations

Abstract

In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is (2−α) for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme.