Uniformly convergent numerical method for time-fractional convection–diffusion equation with variable coefficients

Abstract

This paper presents a uniformly convergent numerical scheme for singularly perturbed fractional order convection–diffusion equations with variable coefficients. First, the time-fractional derivative is considered in the Caputo sense and treated using the implicit Euler method. Then, a uniformly convergent numerical scheme based on the nonstandard finite difference method is developed. The technique is proved rigorously for parameter-uniform convergence. By numerical experimentation, it is also validated that the computational results agree with theoretical results.