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

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  20 June 2017

Cuicui Ji  and
Zhizhong Sun
Cuicui Ji
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, P. R. China
Zhizhong Sun*
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, P. R. China
*
*Corresponding author. Email address:zzsun@seu.edu.cn (Z. Z. Sun)
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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 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.

Keywords

Stokes’ first problemheat flowfractional derivativefinite difference schemeunconditional stabilityconvergence

MSC classification

Secondary: 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods 65M15: Error bounds 35R11: Fractional partial differential equations
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 3 , August 2017 , pp. 597 - 613
Copyright
Copyright © Global-Science Press 2017 

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