High order fitted operator numerical method for self-adjoint singular perturbation problems

Applied Mathematics and Computation

Volumn 171, Issue 1, 2005, Pages 547-566

  Patidar, Kailash C ^a  

^a UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

Boundary value problems; Finite difference methods; Fitted operator methods; Numerov's method; Ordinary differential equations; Singular perturbation problems

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; MATRIX ALGEBRA; ORDINARY DIFFERENTIAL EQUATIONS; PARAMETER ESTIMATION;

NUMEROV'S METHODS; OPERATOR METHODS; OPERATOR NUMERICAL METHOD; SELF-ADJOINT SINGULAR PERTURBATION PROBLEMS;

NUMERICAL METHODS;

EID: 28444453616     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.01.069     Document Type: Article

References (31)

1. D. Allien, and R.V. Southwell Relaxation methods applied to determine the motion in 2-D of a viscous fluid past a fixed cylinder Quart. J. Mech. Appl. Math. VIII 2 1955 129 145
2. A.E. Berger, J.M. Solomon, M. Ciment, S.H. Leventhal, and B.C. Weinberg Generalized operator compact implicit schemes for boundary layer problems Math. Comput. 35 1980 695 731
3. I.P. Boglaev A variational difference scheme for a boundary value problem with a small parameter in the highest derivative USSR Comput. Math. Math. Phys. 21 4 1981 71 81
4. J.H. Bramble, and B.E. Hubbard On a finite difference analogue of an elliptic boundary problem which is neither diagonally dominant nor of non-negative type J. Math. Phys. 43 1964 117 132
5. K.W. Chang, and F.A. Howes Nonlinear Singular Perturbation Phenomena: Theory and Application 1984 Springer-Verlag New York
6. E.P. Doolan, J.J.H. Miller, and W.H.A. Schilders Uniform Numerical Methods for Problems with Initial and Boundary Layers 1980 Boole Press Dublin
7. P.A. Farrell, A. Hegarty, J.J.H. Miller, E. O'Riordan, and G.I. Shishkin Robust Computational Techniques for Boundary Layers 2000 Chapman & Hall/CRC New York
8. M.K. Jain Numerical Solution of Differential Equations 1984 Wiley New York
9. M.K. Kadalbajoo, and K.C. Patidar A survey of numerical techniques for solving singularly perturbed ordinary differential equations Appl. Math. Comput. 130 2-3 2002 457 510
10. M.K. Kadalbajoo, and K.C. Patidar Singularly perturbed problems in partial differential equations: a survey Appl. Math. Comput. 134 2-3 2003 371 429
11. J. Kevorkian, and J.D. Cole Perturbation Methods in Applied Mathematics 1981 Springer-Verlag New York
12. J. Kevorkian, and J.D. Cole Multiple Scale and Singular Perturbation Methods 1996 Springer-Verlag New York
13. J.D. Lambert Computational Methods in Ordinary Differential Equations 1973 John Wiley & Sons New York
14. W. Liniger, R.A. Willoughby, Efficient numerical integration methods for stiff system of differential equations, IBM Research Report RC-1970, 1967.
15. J.J.H. Miller On the convergence, uniformly in ε, of difference schemes for a two-point boundary singular perturbation problem Numerical Analysis of Singular Perturbation Problems 1979 Academic Press New York 467 474
16. J.J.H. Miller, E. O'Riordan, and G.I. Shishkin Fitted Numerical Methods for Singular Perturbation Problems 1996 World Scientific Singapore
17. K.W. Morton Numerical Solution of Convection-diffusion Problems 1996 Chapman & Hall London
18. A.H. Nayfeh Perturbation Methods 1973 Wiley New York
19. A.H. Nayfeh Introduction to Perturbation Techniques 1981 John Wiley & Sons New York
20. K. Niijima On a three-point difference scheme for a singular perturbation problem without a first derivative term I Mem. Numer. Math. 7 1980 1 10
21. R.E. O'Malley Introductions to Singular Perturbations 1974 Academic Press New York
22. R.E. O'Malley Singular Perturbation Methods for Ordinary Differential Equations 1991 Springer-Verlag New York
23. E. O'Riordan, and M. Stynes A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion problem Math. Comput. 47 1986 555 570
24. H.-G. Roos Global uniformly convergent schemes for a singularly perturbed boundary-value problem using patched base spline-functions J. Comput. Appl. Math. 29 1 1990 69 77
25. H.-G. Roos, M. Stynes, and L. Tobiska Numerical Methods for Singularly Perturbed Differential Equations 1996 Springer
26. A.H. Schatz, and L.B. Wahlbin On the finite element method for singularly perturbed reaction diffusion problems in two and one dimension Math. Comput. 40 1983 47 89
27. M. Stojanović A uniformly accurate spline collocation method for a singular perturbation problem Calcolo 27 1-2 1990 81 88
28. M. Stojanović Exponential splines difference scheme for singular perturbation problem with mixed boundary conditions Commun. Appl. Numer. Meth. 7 8 1991 625 632
29. J.M. Varah A lower bound for the smallest singular value of a matrix Linear Alg. Appl. 11 1975 3 5
30. R.S. Varga Matrix Iterative Analysis 1962 Prentice-Hall Englewood Cliffs, NJ
31. V. Vukoslavčević, and K. Surla Finite element method for solving self adjoint singularly perturbed boundary value problems Mathematica Montisnigri VII 1996 86 89