An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes’ First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

This article is intended to fill in the blank of the numerical schemes with second-order convergence accuracy in time for nonlinear Stokes’ first problem for a heated generalized second grade fluid with fractional derivative. A linearized difference scheme is proposed. The time fractional-order derivative is discretized by second-order shifted and weighted Gr¨unwald-Letnikov difference operator. The convergence accuracy in space is improved by performing the average operator. The presented numerical method is unconditionally stable with the global convergence order of in maximum norm, where τ and h are the step sizes in time and space, respectively. Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is efficient indeed.