A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative

Authors:
Chang-Ming Chen;F. Liu;V. Anh
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia and School of Mathematical Sciences, South China University of Technology, Guangz ...;School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this article, we consider Stokes' first problem for a heated generalized second grade fluid with fractional derivative (SFP-HGSGF). Implicit and explicit numerical approximation schemes for the SFP-HGSGF are presented. The stability and convergence of the numerical schemes are discussed using a Fourier method. In addition, the solvability of the implicit numerical approximation scheme is also analyzed. A Richardson extrapolation technique for improving the order of convergence of the implicit scheme is proposed. Finally, a numerical test is given. The numerical results demonstrate the good performance of our theoretical analysis.