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

✍ Scribed by Chang-Ming Chen; F. Liu; V. Anh

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 579 KB
• Volume: 223
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.03.001

✦ Synopsis

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.