Fitted mesh B-spline collocation method for solving self-adjoint singularly perturbed boundary value problems

Applied Mathematics and Computation

Volumn 161, Issue 3, 2005, Pages 973-987

  Kadalbajoo, Mohan K ^a   Aggarwal, Vivek K ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

B spline collocation method; Boundary layers; Fitted mesh method; Self adjoint singularly perturbed boundary value problems; Uniform convergence

Indexed keywords

BOUNDARY LAYERS; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; LINEAR SYSTEMS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

B-SPLINE COLLACATION METHOD; FITTED MESH METHOD; SELF-ADJOINT SINGULARLY PERTURBED VALUE PROBLEMS; UNIFORM CONVERGENCE;

BOUNDARY VALUE PROBLEMS;

EID: 10644233764     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.12.078     Document Type: Article

References (13)

1. M.H. Potter, H.F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1967.
2. I.P. Boglaev, A variational difference scheme for a boundary value problems with a small parameter in the highest derivative, USSR, Comput. Math. Math. Phys. 21 (4) (1981) 71-81.
3. A.H. Schatz, 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.
4. K. Niijima, On a three-point difference scheme for a singular perturbation problem without a first derivative term II, Mem. Numer. Math. 7 (1980) 11-27.
5. 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.
6. J.J.H. Miller, On the convergence, uniformly in ∈, of difference schemes for a two-point boundary singular perturbation problem, in: Numerical Analysis of Singular Perturbation Problems, Academic Press, New York, 1979, pp. 467-474.
7. K. Surla, V. Jerkovic, Some possibilities of applying spline collocations to singular perturbation problems, Numerical methods and Approximation Theory, vol. II, Novisad, 1985, pp 19-25.
8. M. Sakai, R.A. Usmani, On exponential splines, J. Approx. Theory 47 (1986) 122-131.
9. L.L. Schumaker, Spline Functions: Basic Theory, Krieger Publishing Company, Florida, 1981.
10. J.M. Ahlberg, E.N. Nilson, J.L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York, 1967.
11. G. Micula, Handbook of Splines, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
12. E.P. Doolan, J.J.H. Miller, W.H.A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.
13. V. Vukoslavcevic, K. Surla, Finite element method for solving self-adjoint singularly perturbed boundary value problems, Math. Montisnigri. VII (1996) 69-86.