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A Fourier method and an extrapolation technique for Stokes’ first problem for a heated generalized second-grade fluid with fractional derivative. (English) Zbl 1153.76049
Summary: 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 good performance of our theoretical analysis.
76M25Other numerical methods (fluid mechanics)
76A10Viscoelastic fluids
80A20Heat and mass transfer, heat flow