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

Journal of Computational and Applied Mathematics

Volumn 223, Issue 2, 2009, Pages 777-789

  Chen, Chang Ming ^a   Liu, F ^b,c   Anh, V ^b  

^a XIAMEN UNIVERSITY   (China)

^b QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

^c SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Convergence; Extrapolation method; Fourier method; Heat flow; Numerical approximation; Stability; Stokes' first problem

Indexed keywords

APPROXIMATION THEORY; ELECTRIC NETWORK ANALYSIS; EXTRAPOLATION; POLYNOMIAL APPROXIMATION; WALL FLOW;

CONVERGENCE; EXTRAPOLATION METHOD; FOURIER METHOD; HEAT FLOW; NUMERICAL APPROXIMATION; STOKES' FIRST PROBLEM;

CONVERGENCE OF NUMERICAL METHODS;

EID: 56949093590     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.03.001     Document Type: Article

References (26)

1. Chen C.-M., Liu F., Turner I., and Anh V. A Fourier method for the fractional diffusion equation describing sub-diffusion. J. Comput. Phys. 227 (2007) 886-897
2. Chen C.-M., Liu F., Turner I., and Anh V. A new Fourier analysis method for the Galilei invariant fractional advection diffusion equation. ANZIAM J. 48 C605-619 (2007)
3. Fetecau C., and Conna F. The Rayleigh-Stokes problem for heated second grade fluids. Internat. J. Non-Linear Mech. 37 (2002) 1011-1015
4. Langlands T.A.M., and Henry B.I. The accuracy and stability of an implicit solution method for the fractional diffusion equation. J. Comput. Phys. 205 (2005) 719-736
5. Liu F., Anh V., and Turner I. Numerical Solution of the Space Fractional Fokker-Planck Equation. J. Comput. Appl. Math. 166 (2004) 209-219
6. Liu F., Anh V., Turner I., and Zhuang P. Numerical simulation for solute transport in fractal porous media. ANZIAM J. 45(E) (2004) 461-473
7. Liu F., Shen S., Anh V., and Turner I. Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation. ANZIAM J. 46(E) (2005) 488-504
8. Liu F., Zhuang P., Anh V., Turner I., and Burrage K. Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. J. Appl. Math. Comput. 191 (2007) 12-21
9. Liu Q., Liu F., Turner I., and Anh V. Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method. J. Comput. Phys. 222 (2007) 57-70
10. Meerschaert M., and Tadjeran C. Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 172 (2004) 65-77
11. Rajagopal K.R. On the decay of vortices in a second grade fluid. Meccanica 9 (1980) 185-188
12. Rajagopal K.R., and Gupta A.S. On a class of exact solution to the equations of motion of a second grade fluid. Internat. J. Eng. Sci. 19 (1981) 1009-1014
13. 2. J. Comput. Appl. Math. 193 1 (2006) 243-268
14. Shen F., Tan W.C., Zhao Y., and Masuoka T. The Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative model. Nonlinear Anal. RWA 7 5 (2006) 1072-1080
15. Shen S., and Liu F. Error analysis of an explicit finite difference approximation for the space fractional diffusion. ANZIAM J. 46(E) (2005) 871-887
16. Tan W.C., and Xu M.Y. Plate surface suddenly set in motion in a vicoelastic fluid with fractional Maxwell model. Acta Mech. Sin. 18 (2002) 342-349
17. Tan W.C., and Xu M.Y. The impulsive motion of flat plate in a general second grade fluid. Mech. Res. Commun. 29 (2002) 3-9
18. Tan W.C., Pan W.X., and Xu M.Y. A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates. Internat. J. Non-Linear Mech. 38 (2003) 645-650
19. Tan W.C., and Xu M.Y. Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates. Acta Mech. Sin. (2004) 471-476
20. Tan W.C., and Masuoka T. Stokes' first problem for a second grade fluid in a porous half-space with heated boundary. Internat. J. Non-Linear Mech. 40 (2005) 515-522
21. Q. Yu, F. Liu, V. Anh, I. Turner, Solving linear and nonlinear space-time fractional reaction-diffusion equations by Adomian decomposition method, Internat. J. Numer. Meth. Eng. (2007) (in press)
22. Yuste S.B., and Acedo L. An explicit finite difference method and a new Von Neumann-type stability analysis for fractional diffusion equations. SIAM J. Numer. Anal. 42 5 (2005) 1862-1874
23. Zhuang P., and Liu F. Implicit difference approximation for the time fractional diffusion equation. J. Appl. Math. Comput. 22 3 (2006) 87-99
24. Diethelm K., and Walz G. Numerical solution of fractional order differential equations by extrapolation. Numer. Algorithms 16 (1997) 231-251
25. Diethelm K., Ford N.J., Feed A.D., and Luchko Yu. Algorithms for the fractional calculus: A selection of numerical methods. Comput. Methods Appl. Mech. Eng. 194 (2005) 743-773
26. Tadjeran C., and Mark M. Meerschaert, Hans-Petter Scheffier, A second order accurate numerical approximation for the fractional diffution equation. J. Comput. Phys. 213 (2006) 205-213