Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 597-613.
Published online: 2017-10
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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-Letnikovv 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 $\mathcal{O}(τ^2+h^4)$ 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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.m1605}, url = {http://global-sci.org/intro/article_detail/nmtma/12360.html} }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-Letnikovv 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 $\mathcal{O}(τ^2+h^4)$ 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.