The Finite Difference Method and Analysis for Simulating the Unsteady Generalized Maxwell Fluid with a Multi-Term Time Fractional Derivative

The finite difference method is used to solve a new class of unsteady generalized Maxwell fluid models with multi-term time-fractional derivatives. The fractional order range of the Maxwell model index is from 0 to 2, which is hard to approximate with general methods. In this paper, we propose a new finite difference scheme to solve such problems. Based on the discrete H1 norm, the stability and convergence of the considered discrete scheme are discussed. We also prove that the accuracy of the method proposed in this paper is O(τ+h2). Finally, some numerical examples are provided to further demonstrate the superiority of this method through comparative analysis with other algorithms.