An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes' First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative
Year: 2017
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 597–613
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2017.m1605
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 597–613
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
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