Numerical solution of singularly perturbed two-point boundary value problems by spline in tension

Applied Mathematics and Computation

Volumn 131, Issue 2-3, 2002, Pages 299-320

  Kadalbajoo, Mohan K ^a   Patidar, Kailash C ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

BVPs; ODEs; Singular perturbation; Spline in tension

Indexed keywords

EID: 0037174256     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(01)00146-1     Document Type: Article

References (14)

1. L.R. Abrahamsson H.B. Keller H.-O. Kreiss Difference approximations for singular perturbations of the system of ordinary differential equations Numer. Math. 22 1974 367 391
2. A.E. Berger J.M. Solomon M. Ciment An analysis of a uniformly accurate difference method for a singular perturbation problem Math. Comput. 37 1981 79 94
3. R.C. Chin R. Krasny A hybrid asymptotic finite element method for stiff two-point boundary value problems SIAM J. Sci. Stat. Comput. 4 2 1983 229 243
4. C. de Boor, A Practical Guide to Splines, Applied Mathematical Science Series 27, Springer, New York, 1978
5. P.P.N. de Groen P.W. Hemker Error bounds for exponentially fitted galerkin methods applied to stiff two-point boundary value problems P.W. Hemker J.J.H. Miller Numerical Analysis of Singular Perturbation Problems 1979 Academic Press New York 217 249
6. E.P. Doolan J.J.H. Miller W.H.A. Schilders Uniform Numerical Methods for Problems with Initial and Boundary Layers 1980 Boole Press Dublin
7. C.G. Eugene Jr. Uniformly high-order difference schemes for a singularly perturbed two-point boundary value problem Math. Comput. 48 178 1987 551 564
8. R.B. Kellogg A. Tsan Analysis of some difference approximations for a singular perturbation problem without turning points Math. Comput. 32 1978 1025 1039
9. B. Kreiss H.-O. Kreiss Numerical methods for singular perturbation problems SIAM J. Numer. Anal. 46 1982 138 165
10. J. Lorenz Combination of initial and boundary value methods for a class of singular perturbation problems P.W. Hemker J.J.H. Miller Numerical Analysis of Singular Perturbation Problems 1979 Academic Press New York 295 315
11. R.E. O'Malley Jr. Introduction to Singular Perturbations 1974 Academic Press New York
12. S. Pruess Properties of splines in tension J. Approx. Theory 17 1976 86 96
13. D. Schweikert An interpolation curve using splines in tension J. Math. Phys. 45 1966 312 317
14. V. Vukoslavčević K. Surla Finite element method for solving self adjoint singularly perturbed boundary value problems Mathematica Montisnigri VII 1996 86 89