Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes' first problem for a heated generalized second grade fluid

Authors:
Chang-Ming Chen;F. Liu;I. Turner;V. Anh
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;School of Mathematical Sciences, Xiamen University, Xiamen 361005, China and Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia;Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia;Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

Stokes' first problem has in recent years received much attention. In this paper, we focus on the variable-order nonlinear Stokes' first problem for a heated generalized second grade fluid. A numerical scheme with fourth-order spatial accuracy is developed to solve the problem. The stability, solvability and convergence of the numerical scheme are discussed via Fourier analysis. An improved numerical scheme is also developed. In addition, a numerical example is given and the numerical results support the effectiveness of our theoretical analysis results.