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

摘要

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 Grünwald-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 (σ)(τ2 + h4) 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.