A modified Chebyshev pseudospectral DD algorithm for the GBH equation

Computers and Mathematics with Applications

Volumn 62, Issue 9, 2011, Pages 3366-3377

  Javidi, M ^a  

^a RAZI UNIVERSITY   (Iran)

Author keywords

Domain decomposition; Generalized Burger'sHuxley equation; Grid mapping; Pseudospectral method

Indexed keywords

CHEBYSHEV; CHEBYSHEV SPECTRAL COLLOCATION METHOD; DIFFERENTIAL ALGEBRAIC EQUATIONS; DOMAIN DECOMPOSITIONS; FOURTH ORDER; GENERALIZED BURGER'SHUXLEY EQUATION; GRID MAPPING; NUMERICAL INTEGRATIONS; NUMERICAL SOLUTION; PSEUDOSPECTRAL; PSEUDOSPECTRAL METHODS; ROUND-OFF ERRORS; RUNGE-KUTTA FORMULA; SEMIDISCRETIZATION; SPECTRAL COLLOCATION;

ALGEBRA; DOMAIN DECOMPOSITION METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

PHOTOMAPPING;

EID: 80054709428     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.08.051     Document Type: Article

References (25)

1. M. Javidi, and A. Golbabai A new domain decomposition algorithm for generalized Burger'sHuxley equation based on Chebyshev polynomials and preconditioning Chaos Solitons Fractals 39 2 2009 849 857
2. X.Y. Wang, Z.S. Zhu, and Y.K. Lu Solitary wave solutions of the generalized Burger'sHuxley equation J. Phys. A: Math. Gen. 23 1990 271 274 Printed in the UK
3. A.L. Hodgkin, and A.F. Huxley A quantitative description of membrane current and its application to conduction and excitation in nerve J. Physiol. 117 1952 500 544
4. R. Fitzhugh Mathematical models of excitation and propagation in nerve H.P. Schwan, Biological Engineering 1969 McGraw-Hill New York 1 85
5. A. Golbabai, and M. Javidi A spectral domain decomposition approach for the generalized Burger'sFisher equation Chaos Solitons Fractals 39 1 2009 385 392
6. H.N.A. Ismail, K. Raslan, and A.A.A. Rabboh Adomian decomposition method for Burger's Huxley and Burger'sFisher equations Appl. Math. Comput. 159 2004 291 301
7. P.G. Estevez Non-classical symmetries and the singular modified the Burger's and Burger'sHuxley equation J. Phys. A 27 1994 2113 2127
8. A. Kaushik, and M.D. Sharma A uniformly convergent numerical method on non-uniform mesh for singularly perturbed unsteady Burger'sHuxley equation Appl. Math. Comput. 195 2 2008 688 706
9. R. Baltensperger, and M.R. Trummer Spectral differencing with a twist SIAM J. Sci. Comput. 24 5 2003 1465 1487
10. J.P. Boyd Chebyshev and Fourier Spectral Methods Lecture Notes in Engineering vol. 49 1989 Springer-Verlag Berlin
11. C. Canuto, A. Quarteroni, M.Y. Hussaini, and T. Zang Spectral Method in Fluid Mechanics 1988 Springer-Verlag New York
12. W.S. Don, and A. Solomonoff Accuracy and speed in computing the Chebyshev collocation derivative SIAM J. Sci. Comput. 16 4 1995 1253 1268
13. L.N. Trefethen Spectral Methods in MATLAB 2000 SIAM Philadelphia
14. A. Bayliss, A. Class, and B.J. Matkowsky Roundoff error in computing derivatives using the Chebyshev differentiation matrix J. Comput. Phys. 116 1995 380 383
15. B. Fornberg Generation of finite difference formulas on arbitrarily spaced grids Math. Comp. 51 1988 699 706
16. J.A.C. Weideman, and S.C. Reddy A MATLAB differentiation matrix suite Trans. Math. Softw. 26 2000 465 519
17. B.D. Welfert Generation of pseudospectral differentiation matrices, I SIAM J. Numer. Anal. 34 1977 1640 1657
18. M. Javidi, and A. Golbabai Numerical studies on nonlinear Schrodinger equations by spectral collocation method with preconditioning J. Math. Anal. Appl. 333 2 2007 1119 1127
19. A. Khater, R.S. Temsah, and M.M. Hassan A Chbyshev spectral collocation method for solving Burgers'-type equations J. Comput. Appl. Math. 222 2 2008 333 350
20. A. Karageorghis, and T. Tang A spectral domain decomposition approach for steady NavierStokes problems in circular geometries Comput. Fluids 25 6 1996 541 549
21. M. Israeli domain decomposition methods for solving parabolic PDEs on multiprocessors Appl. Numer. Methods 1993 135 149
22. A. Karageorghis, and T.N. Phillips On efficient direct methods for conforming spectral domain decomposition techniques J. Comput. Appl. Math. 33 2 1990 141 155
23. A. Karageorghis, and S. Sivaloganathan Conforming spectral approximations for non-conforming domain decompositions Comput. Methods Appl. Mech. Engrg. 156 14 1998 299 308
24. B. Bialecki A nonoverlapping domain decomposition method for Legendre spectral collocation problems J. Sci. Comput. 32 2 2007 373 409
25. 1) time step restriction J. Comput. Phys. 104 2 1993 457 469