Analytical and numerical solutions of a multi-term time-fractional Burgers’ fluid model

Abstract

In this paper, we consider a multi-term time-fractional Burgers’ fluid model (MT-TFBFM). The analytical solution of MT-TFBFM is obtained by the method of separation of variables. We present a unified numerical scheme by virtue of the weighted shifted Grünwald difference (WSGD) scheme in time and Legendre spectral method in space. Especially, the corrected weighted shifted Grünwald difference (CWSGD) scheme is utilized to improve the convergence accuracy. Three examples are given to illustrate the stability, accuracy and effectiveness of the proposed numerical scheme.