Initial value technique for singularly perturbed two point boundary value problems using an exponentially fitted finite difference scheme

Computers and Mathematics with Applications

Volumn 57, Issue 7, 2009, Pages 1147-1156

  Kadalbajoo, Mohan K ^a   Kumar, Devendra ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Boundary layer; Boundary value problems; Exponential fitted finite difference scheme; Ordinary differential equations; Singular perturbation problems

Indexed keywords

AERODYNAMICS; ASYMPTOTIC ANALYSIS; BOUNDARY LAYER FLOW; BOUNDARY LAYERS; DIFFERENCE EQUATIONS; DYNAMICAL SYSTEMS; INITIAL VALUE PROBLEMS; PERTURBATION TECHNIQUES; PREDICTIVE CONTROL SYSTEMS;

APPROXIMATE METHODS; ASYMPTOTIC BEHAVIORS; ASYMPTOTIC EXPANSIONS; BOUNDARY VALUE PROBLEMS; EXACT SOLUTIONS; EXPONENTIAL FITTED FINITE DIFFERENCE SCHEME; EXPONENTIALLY FITTED FINITE DIFFERENCE SCHEMES; FIRST ORDERS; INITIAL VALUE TECHNIQUES; INITIAL VALUES; MESH SIZES; NUMERICAL EXAMPLES; NUMERICAL SOLUTIONS; QUASI-LINEAR; SINGULAR PERTURBATION PROBLEMS; SINGULARLY PERTURBED; TWO POINT BOUNDARY VALUE PROBLEMS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 61749091523     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.01.010     Document Type: Article

References (19)

1. O'Malley R.E. Introduction to Singular Perturbations (1974), Academic Press, New York
2. O'Mally R.E. Singular Perturbation Methods for Ordinary Differential Equations (1991), Springer, New York
3. Nayfeh A.H. Perturbation Methods (1973), Wiley, New York
4. Nayfeh A.H. Introduction to Perturbation Techniques (1981), Wiley, New York
5. Cole J.D., and Kevorkian J. Perturbation Methods in Applied Mathematics (1979), Springer, New York
6. Bender C.M., and Orszag S.A. Advanced Mathematical Methods for Scientist and Engineers (1978), McGraw-Hill, New York
7. Eckhaus W. Matched Asymptotic Expansions and Singular Perturbations (1973), North- Holland, Amsterdam
8. Van Dyke M. Perturbation Methods in Fluid Mechanics (1975), Parabolic Press, Stanford, CA
9. Bellman R. Perturbation Techniques in Mathematics, Physics and Engineering (1964), Holt, Rinehart & Winston, New York
10. Ascher U., and Weis R. Collocation for singular perturbation problem III: Non-linear problems without turning points. SIAM J. Sci. Stat. Comput. 5 (1984) 811-829
11. Lin P., and Su Y. Numerical solution of quasilinear singularly perturbed ordinary differential equation without turning points. Appl. Math. Mech. 10 (1989) 1005-1010
12. Vulanovic R. A uniform numerical method for quasilinear singular perturbation problems without turning points. Computing 41 (1989) 97-106
13. Vulanovic R. A second order numerical method for nonlinear singular perturbation problems without turning points. Zh. Vychisl. Mat. Mat. Fiz. 31 (1991) 522-532
14. Roos H.G. A second order monotone upwind scheme. Computing 36 (1986) 57-67
15. Doolan E.P., Miller J.J.H., and Schilders W.H.A. Uniform Numerical Methods for Problems with Initial and Boundary Layers (1980), Boole Press, Dublin
16. Farrell P.A., Hegarty A.F., Miller J.J.H., O'riordan R.E., and Shishkin G.I. Robust Computational Techniques for Boundary Layers (2000), Chapman- Hall/CRC, New York
17. Keller H.B. Numerical Methods for Two Point Boundary Value Problems (1968), Ginn-Blaisdell, New York
18. Kadalbajoo M.K., and Reddy Y.N. An approximate method for solving a class of singular perturbation problems. J. Math. Anal. Appl. 133 (1988) 306-323
19. Reinhardt H.J., Hsiao G.C., Abrahamsson L.R., Keller H.B., and Kreiss O. Singular perturbations of difference methods for linear ordinary differential equations. Appl. Anal. 10 (1980) 53-70