Stability Analysis According to the Regularity of External Forces of a Semi-Implicit Difference Scheme for Time Fractional Navier–Stokes Equations

Abstract

In this paper, we discuss the stability of a semi-discrete implicit difference scheme of the time fractional Navier–Stokes equations which is applied in many physical processes, and the convergence of the difference approximate solution. First, we introduce the concept of the average characteristic of the sequence obtained by the difference scheme and the concept of partial stability of the scheme, and then obtain several stability results according to the normality of the external force term. We also prove the convergence of the difference approximation sequence to the unique solution of the equation.