On the solution a of second order singularly-perturbed boundary value problem by the Sinc-Galerkin method

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 56, Issue 1, 2005, Pages 45-58

  El Gamel, Mohamed ^a   Cannon, John R ^b  

^a Mansoura University   (Egypt)

^b UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Numerical solutions; Sinc function; Sinc Galerkin; Singularly perturbed

Indexed keywords

EID: 12444327306     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-004-3002-6     Document Type: Article

References (32)

1. G. Adomian, A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., 102 (1984), 420-434.
2. T. Aziz and A. Khan, A spline method for second-order singularly perturbed boundary-value problems, J. Comp. Appl. Math. 147 (2002) 445-452.
3. N. Bellman, Introduction to Matrix Analysis, Mc Graw-Hill, Inc., New York 1960.
4. B. Bialecki, Sinc-Collocation methods for two-point boundary value problems, IMA J. Numer. Anal. 11 (1991) 357-375.
5. K. Bowers et al., Advection-diffusion equation: Temporal Sinc methods, Numer. Meth. Part. Diff. Eq., 11 (1995) 399-422.
6. C. G. Broyden, The convergence of an algorithm for solving sparse nonlinear systems, Math. Comp., 25 (1971), 285-294.
7. R. L. Burden and J.D. Faires, Numerical Analysis, PWS, Boston 1993.
8. G. Dahlquist, A. Bjorck and N. Anderson, Numerical Methods, Prentice-Hall, Englewood Cuffs, NJ 1974.
9. G. H. Dee and W. van Saarloos, Bistable systems with propagating fronts leading to pattern formation, Phys. Rev. Lett., 60 (1988), 2641-2644.
10. M. El-Gamel, J. R. Cannon and A. Zayed, Sinc-Galerkin method for solving linear sixth order boundary-value problems, Math. Comp. (to appear)
11. M. El-Gamel and A. Zayed, A comparison between the Wavelet-Galerkin and the Sinc-Galerkin methods in solving nonhomogeneous heat equations, Contemporary Mathematics of the American Mathematical Society, Series, Inverse Problem, Image Analysis, and medical Imaging Edited by Zuhair Nashed and Otmar Scherzer, Vol. 313, AMS, Providence, 2002.
12. M. El-Gamel, S. Behiry and H. Hashish, Numerical method for the solution of special non-linear fourth-order boundary value problems, Appl. Math. Comp. 145 (2003), 717-734.
13. G. H. Golub and C. F. Van Loan, Matrix Computations, Second Ed., Johns Hopkins University Press, Baltimore 1989.
14. S. Gonzalez-Pinto et al. A numerical scheme to approximate the solution of a singularly perturbed nonlinear differential equation, J. Comp. Appl. Math. 35 (1991), 217-225.
15. V. Grenander and G. Szego, Toeplitz Forms and Their Applications, Second Ed. Chelsea Publishing Co., Orlando 1985.
16. M. E. Herniter, Programming in Matlab, Bill Stenquist, 2001.
17. D. Jespersen, Ritz-Galerkin methods for singular boundary value problems, Math. Research Center Tech. Rep. 1972, Univ. of Wisconsin, Madison 1977.
18. L. Jiang et al., Local exponentially fitted finite element schemes for singularly perturbed convection-diffusion problems, J. Comp. Appl. Math.132 (2001), 277-293.
19. J. Lund, Symmetrization of the Sinc-Galerkin method for boundary value problems, Math. Comp., 47 (1986), 571-588.
20. J. Lund and K. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, PA 1992.
21. M. Kadalbajoo and A. Rao, The Alternating Group Explicit (AGE) method for singularly perturbed boundary value problems, Appl. Math. Comp. 68 (1995), 125-142.
22. J. Kevorkian and J. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, 1981.
23. K. Michael, Fast iterative methods for symmetric Sinc-Galerkin system, IMA J. Numer. Anal. 19 (1999), 357-373.
24. H. Neudecker, A note on Kronecker matrix products and matrix equation systems, SIAM J. Appl. Math. 17 (1969), 603-606.
25. R. O'Malley, Jr. Singular Perturbation Methods for Ordinary Differential Equations, Springer-Verlag, 1991.
26. C. Ralph and K. Bowers, The Sinc-Galerkin method for fourth-order differential equations, SIAM J. Numer. Anal. 28 (1991), 760-788.
27. Y. Reddy and P. Chakravrth, Method of reduction of order for solving singularly perturbed two point boundary value problems, Appl. Math. Comp. 136 (2003), 27-45.
28. H. G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations, Springer-Verlag, 1996.
29. A. Singh, A numerical method for singularly perturbed systems of linear two point boundary value problems using partial decoupling, J. Comp. Appl. Math. 40 (192) 55-62.
30. F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer, New York 1993.
31. G. Yin, Sinc-Collocation method with orthogonalization for a singular Poisson-like problem, Math. comput. 62 (1994) 21-40.
32. A.I. Zayed, Advances in Shannon's Sampling Theory, CRS Press, Boca Raton 1993.