A numerical solution of Burgers' equation by pseudospectral method and Darvishi's preconditioning

Applied Mathematics and Computation

Volumn 173, Issue 1, 2006, Pages 421-429

  Darvishi, M T ^a   Javidi, M ^a  

^a RAZI UNIVERSITY   (Iran)

Author keywords

Burgers' equation; Preconditioning; Pseudospectral

Indexed keywords

COMPUTATION THEORY; ERROR DETECTION; NUMERICAL METHODS; PROBLEM SOLVING; VISCOSITY;

BURGERS' EQUATIONS; NUMERICAL RESULTS; PRECONDITIONING; PSEUDOSPECTRAL;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 32144446303     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.04.079     Document Type: Article

References (20)

1. S. Abbasbandy, and M.T. Darvishi A numerical solution of Burgers' equation by modified Adomian method Appl. Math. Comput. 163 2005 1265 1272
2. S. Abbasbandy, M.T. Darvishi, A numerical solution of Burgers' equation by time discretization of Adomian method, Appl. Math. Comput., in press, doi:10.1016/j.amc.2004.10.060.
3. E.N. Aksan, and A. Özdeş A numerical solution of Burgers' equation Appl. Math. Comput. 156 2004 395 402
4. C. Bernardi, and Y. Maday Some spectral approximations of one-dimensional fourth-order problems P. Nevai A. Pinkus Progress in Approximation Theory 1991 Academic press Boston
5. J.P. Boyd Chebyshev and Fourier spectral methods Lecture Notes in Engineering 49 1989 Springer-Verlag Berlin
6. M. Berzins Global error estimation in the methods of lines for parabolic equations Siam J. Sci. Stat. Comput. 19 4 1988 687 701
7. J.M. Burger A mathematical model illustrating the theory of turbulence Adv. Appl. Math. 1 1947 171 179
8. C. Canuto, A. Quarteroni, M.Y. Hussaini, and T. Zang Spectral Method in Fluid Mechanics 1988 Springer-Verlag New York
9. J.D. Cole On a quasilinear parabolic equations occuring in aerodynamics Quart. Appl. Math. 9 1951 225 236
10. M.T. Darvishi, and F. Ghoreishi Error reduction for higher derivatives of Chebyshev collocation method using preconditioning and domain decomposition Korean J. Comput. Appl. Math. 6 2 1999 421 435
11. M.T. Darvishi, and F. Ghoreishi Multidomain and preconditioning schemes for computing higher derivatives Far East J. Math. Sci. 1 2 1999 297 316
12. M.T. Darvishi New algorithms for solving ODEs by pseudospectral method Korean J. Comput. Appl. Math. 7 2 2000 319 331
13. M.T. Darvishi Preconditioning and domain decomposition schemes to solve PDEs Int. J. Pure Appl. Math. 1 4 2004 419 439
14. W.S. Don, and A. Solomonoff Accuracy and speed in computing the Chebyshev collocation derivative SIAM J. Sci. Comput. 16 4 1995 1253 1268
15. D. Funaro Polynomial Approximation of Differential Equations 1992 Springer-Verlag Berlin
16. xx Commun. Pure Appl. Math. 3 1950 201 230
17. T. Öziş, and E.N. Aksan A finite element approach for solution of Burgers' equation Appl. Math. Comput. 139 2003 417 428
18. T. Öziş, A. Esen, and S. Kutluay Numerical solution of Burgers' equation by quadratic B-spline finite elements Appl. Math. Comput. 165 2005 237 249
19. L.N. Trefethen Spectral Methods in MATLAB 2000 SIAM Philadelphia
20. H. Tal-Ezer Spectral methods in time for hyperbolic equations SIAM J. Numer. Anal. 23 1 1986 11 26