B-spline solution of singular boundary value problems. (English) Zbl 1107.65062

Summary: Homogeneous and non-homogeneous singular boundary value problems (special case) are solved using B-splines. The original differential equation is modified at singular point then the boundary value problem is treated by using B-spline approximation. The method is tested on some model problems from the literature, and the numerical results are compared with exact solution.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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[1] Agarwal, R.P., Boundary value problems for high order differential equations, (1986), World Scientific Singapore · Zbl 0598.65062
[2] de Boor, C., A practical guide to splines, (1978), Springer Verlag New York · Zbl 0406.41003
[3] Çaglar, H.N.; Çaglar, S.H.; Twizell, E.H., The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions, Int. J. comput. math., 71, 373-381, (1999) · Zbl 0929.65048
[4] Çaglar, H.N.; Çaglar, S.H.; Twizell, E.H., The numerical solution of fifth-order boundary-value problems with sixth-degree B-spline functions, Appl. math. lett., 12, 25-30, (1999) · Zbl 0941.65073
[5] Caglar, N.; Caglar, H.; Cagal, B., Spline solution of nonlinear beam problems, J. concrete appl. math., 1, 3, 253-259, (2003) · Zbl 1064.65061
[6] Caglar, H.; Caglar, N.; Elfaituri, K., B-spline interpolation compared with finite element and finite volume methods which applied to two-point boundary value problems, Appl. math. comput., 175, 72-79, (2006) · Zbl 1088.65069
[7] Chawla, M.M.; Katti, C.P., A finite difference method for a class of singular two point boundary value problems, IMA. J. numer. anal., 4, 457-466, (1984) · Zbl 0571.65076
[8] Golub, G.H.; Ortega, J.M., Scientific computing and differential equations, (1992), Academic Press New York and London · Zbl 0749.65041
[9] Ravi Kanth, A.S.V.; Reddy, Y.N., A numerical method for singular boundary value problems via Chebyshev economization, Appl. math. comput., 146, 691-700, (2003) · Zbl 1024.65060
[10] Ravi Kanth, A.S.V.; Reddy, Y.N., Cubic spline for a class of singular two-point boundary value problems, Appl. math. comput., 170, 733-740, (2005) · Zbl 1103.65086
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