A Numerical Method for the Time Fractional Model of Generalised Second Grade Fluid Through Porous Media

Abstract

A numerical method for the generalised second grade fluid through porous media with anomalous diffusion is considered. The method is based on a combination of finite differences in time and a spectral method in space directions. The convergence of the method is rigorously proved and theoretical error estimates are established. The numerical scheme is unconditionally stable and provides a high accuracy if the solution is smooth enough. The results of numerical simulations are consistent with theoretical findings.