Efficient spectral-Petrov-Galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials

Applied Mathematics and Computation

Volumn 218, Issue 15, 2012, Pages 7727-7740

  Doha, E H ^a   Abd Elhameed, W M ^a   Youssri, Y H ^a  

^a CAIRO UNIVERSITY   (Egypt)

Author keywords

Dual Petrov Galerkin method; Generalized Jacobi polynomials; Integrated forms; Nonhomogeneous Dirichlet conditions

Indexed keywords

DUAL-PETROV-GALERKIN METHOD; INTEGRATED FORMS; JACOBI POLYNOMIALS; NON-HOMOGENEOUS; NON-HOMOGENEOUS BOUNDARY CONDITIONS; NUMERICAL RESULTS; PETROV-GALERKIN METHODS;

ALGORITHMS; BOUNDARY CONDITIONS; GALERKIN METHODS; INTEGRATION;

POLYNOMIALS;

EID: 84858332341     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.01.031     Document Type: Article

References (29)

1. G. Szego Orthogonal polynomials Am. Math. Soc. Colloq. Pub. 23 1985
2. B. Bialecki, G. Fairweather, and A. Karageorghis Matrix decomposition algorithms for elliptic boundary value problems: a survey Numer. Algor. 56 2011 3467 3478
3. J.P. Boyd Chebyshev and Fourier Spectral Methods 2nd ed. 2001 Dover Publications Mineola
4. D. Funaro Polynomial Approximation of Differential Equations, Lecturer Notes in Physics 1992 Springer-Verlag Heidelberg,Berlin, New York
5. C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang Spectral Methods in Fluid Dynamics 1988 Springer-Verlag New York
6. L. Fox, and I.B. Parker Chebyshev Polynomials in Numerical Analysis 1972 Oxford University Press Oxford
7. D. Gottlieb, and S.A. Orszag Numerical Analysis of Spectral Methods: Theory and Applications 1977 SIAM Philadelphia
8. R.G. Voigt, D. Gottlieb, and M.Y. Hussaini Spectral Methods for Partial Differential Equations 1984 SIAM Philadelphia
9. B.-Y. Guo, J. Shen, and L.-L. Wang Optimal spectral-Galerkin methods using generalized Jacobi polynomials J. Sci. Comput. 27 2006 305 322 (Pubitemid 43876946)
10. N. Khanal, R. Sharma, and J. Wu A dual-Petrov-Galerkin method for extended fifth-order Kortweg-de Vries type equations Disc. Contin Dynam. Syst., Supplement 2009 442 450
11. C.A. Swanson Comparison and Oscillation Theory of Linear Differential Equations 1968 Academic Press New York
12. Ed. Mckelvey Lectures on Ordinary Differential Equation 1970 Academic Press New York
13. M. Gregus Third Order Linear Differential Equations D 1987 Reidel Publishing Company Dordrecht
14. E.H. Doha, and W.M. Abd-Elhameed Efficient spectral-Galerkin algorithms for direct solution of second-order equations using ultraspherical polynomials SIAM J. Sci. Comput. 24 2002 548 571
15. E.H. Doha, and W.M. Abd-Elhameed Efficient spectral ultraspherical-dual- Petrov-Galerkin algorithms for the direct solution of (2n+1)th-order linear differential equations Math. Comput. Simul. 79 2009 3221 3242
16. E.H. Doha, and A.H. Bhrawy Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials Numer. Algor. 42 2006 137 164 (Pubitemid 44290984)
17. E.H. Doha, and A.H. Bhrawy Efficient spectral-Galerkin algorithms for direct solution of the integrated forms for second-order equations using ultraspherical polynomials ANZIAM J. 48 2007 361 386
18. E.H. Doha, and A.H. Bhrawy Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials Appl. Numer. Math. 58 2008 1224 1244 (Pubitemid 351718463)
19. E.H. Doha, W.M. Abd-Elhameed, and A.H. Bhrawy Efficient spectral ultraspherical-Galerkin algorithms for the direct solution of 2nth-order linear differential equations Appl. Math. Model. 33 2009 1982 1996
20. H. Ma, and W. Sun A Legendre-Petrov-Galerkin method and Chebyshev collocation method for third-order differential equations SIAM J. Numer. Anal. 38 2000 1425 1438 (Pubitemid 33778951)
21. H. Ma, and W. Sun Optimal error estimates of the Legendre-Petrov-Galerkin method for the Kortweg-de Vries equation SIAM J. Numer. Anal. 39 2001 1380 1394
22. T.N. Phillips, and A. Karageoghis On the coefficients of integrated expansions of ultraspherical polynomials SIAM J. Numer. Anal. 27 1990 823 830
23. E.H. Doha On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations J. Comp. Appl. Math. 139 2002 275 298 (Pubitemid 34103368)
24. E.H. Doha Explicit formulae for the coefficients of integrated expansions for Jacobi polynomials and their integrals Integr. Transf. Spec. F 14 2003 69 86 (Pubitemid 36116760)
25. M. Abramowitz, and I.A. Stegun Handbook of Mrathematical Functions Applied Mathematical Series vol. 55 1970 National Bureau of Standards New York
26. G.E. Andrews, R. Askey, and R. Roy Special Functions 1999 Cambridge University Press Cambridge
27. E.H. Doha On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials J. Phys. A: Math. Gen. 37 2004 657 675 (Pubitemid 38148936)
28. J. Shen, T. Tang, and L.L. Wang Spectral Methods: Algorithms, Analysis and Applications, Springer Series in Computational Mathematics 2011 Springer-Verlag Berline. Heidelberg
29. G.W. Stewart Matrix Algorithms, Volume I: Basic Decomposition 1998 SIAM USA