Efficient solutions of multidimensional sixth-order boundary value problems using symmetric generalized Jacobi-Galerkin method

Abstract and Applied Analysis

Volumn 2012, Issue , 2012, Pages

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

^a CAIRO UNIVERSITY   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84862289566     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2012/749370     Document Type: Article

References (28)

1. Doha E. H., Bhrawy A. H., Hafez R. M., A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations Abstract and Applied Analysis 2011 21
2. Bhrawy A. H., Alofi A. S., El-Soubhy S. I., Spectral shifted Jacobi tau and collocation methods for solving fifth-order boundary value problems Abstract and Applied Analysis 2011 2011 14
3. Szeg G., Orthogonal Polynomials 1985 American Mathematical Society Colloquium Publication
4. Andrews G. E., Askey R., Roy R., Special Functions 1999 71 Cambridge, UK Cambridge University Press
5. Boyd J. P., Chebyshev and Fourier Spectral Methods 2001 2nd Mineola, NY Dover Publications
6. Funaro D., Polynomial approximation of differential equations 1992 8 Berlin, Germany Springer Lecture Notes in Physics
7. Canuto C., Hussaini M. Y., Quarteroni A., Zang T. A., Spectral Methods in Fluid Dynamics 1989 New York, NY, USA Springer
8. Boutayeb A., Twizell E. H., Numerical methods for the solution of special sixthorder boundary-value problems International Journal of Computer Mathematics 1992 45 3 207 223
9. Chandrasekhar S., Hydrodynamic and Hydromagnetic Stability 1961 Oxford, UK Clarendon Press
10. Agarwal R. P., Boundary Value Problems for Higher Order Differential Equations 1986 Singapore World Scientific
11. Bhrawy A. H., Legendre-Galerkin method for sixth-order boundary value problems Journal of the Egyptian Mathematical Society 2009 17 2 173 188
12. Lamnii A., Mraoui H., Sbibih D., Tijini A., Zidna A., Spline collocation method for solving linear sixth-order boundary-value problems International Journal of Computer Mathematics 2008 85 11 1673 1684
13. Siddiqi S. S., Twizell E. H., Spline solutions of linear sixth-order boundary-value problems International Journal of Computer Mathematics 1996 60 3-4 295 304 (Pubitemid 126604439)
14. El-Gamel M., Cannon J. R., Zayed A. I., Sinc-Galerkin method for solving linear sixth-order boundary-value problems Mathematics of Computation 2004 73 247 1325 1343 (Pubitemid 38782497)
15. Guo B.-Y., Shen J., Wang L.-L., Optimal spectral-Galerkin methods using generalized Jacobi polynomials Journal of Scientific Computing 2006 27 13 305 322 (Pubitemid 43876946)
16. Doha E. H., Abd-Elhameed W. M., Efficient spectral-Galerkin algorithms for direct solution of second-order equations using ultraspherical polynomials SIAM Journal on Scientific Computing 2002 24 2 548 571
17. Doha E. H., Abd-Elhameed W. M., Efficient spectral ultraspherical-dual- Petrov-Galerkin algorithms for the direct solution of (2 n+1) th-order linear differential equations Mathematics and Computers in Simulation 2009 79 11 3221 3242
18. Doha E. H., Bhrawy A. H., Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials Applied Numerical Mathematics 2008 58 8 1224 1244 (Pubitemid 351718463)
19. Doha E. H., Abd-Elhameed W. M., Bhrawy A. H., Efficient spectral ultraspherical-Galerkin algorithms for the direct solution of 2nth-order linear differential equations Applied Mathematical Modelling 2009 33 4 1982 1996
20. Doha E. H., Abd-Elhameed W. M., Youssri Y. H., Efficient spectral-Petrov-Galerkin methods for third- and fifth-order differential equations using general parameters generalized Jacobi polynomials Quaestiones Mathematicae 2012 218 15 7727 7740
21. Abramowitz M., Stegun I. A., Handbook of Mathematical Functions 1970 55 New York, NY, USA National Bureau of Standards Applied Mathematical Series
22. Doha E. H., The coefficients of differentiated expansions and derivatives of ultraspherical polynomials Computers and Mathematics with Applications 1991 21 2-3 115 122
23. Doha E. H., On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations Journal of Computational and Applied Mathematics 2002 139 2 275 298 (Pubitemid 34103368)
24. Schatzman M., Taylor J., Numerical Analysis: A Mathematical Introduction 2002 Oxford, UK Clarendon Press
25. Doha E. H., On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials Journal of Physics A 2004 37 3 657 675 (Pubitemid 38148936)
26. Graham A., Kronecker Product and Matrix Calculus With Applications 1981 London, UK Ellis Horwood
27. Horn R. A., Johnson C. R., Topics in Matrix Analysis 1991 Cambridge, UK Cambridge University Press
28. Akram G., Siddiqi S. S., Solution of sixth order boundary value problems using non-polynomial spline technique Applied Mathematics and Computation 2006 181 1 708 720 (Pubitemid 44528053)