Spline finite difference methods for singular two point boundary value problems
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In this paper we discuss the construction of a spline function for a class of singular two-point boundary value problemx−α(xαu′)=f (x, u),u(0)=A,u(1)=B, 0<α<1 or α=1,2. The boundary conditions may also be of the formu′(0)=0,u(1)=B. Three point finite difference methods, using the above splines, are obtained for the solution of the boundary value problem. These methods are of second order and are illustrated by four numerical examples.
Subject ClassificationsAMS(MOS): 65L 10 CR: Gl.7
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- 1.Chawla, M.M., Katti, C.P.: Finite difference methods and their convergence for a class of singular two point boundary value problems. Numer. Math.39, 341–350 (1982)Google Scholar
- 2.Ciarlet, P.G., Natterer, F., Varga, R.S.: Numerical methods of high order accuracy for singular nonlinear boundary value problems. Numer. Math.15, 87–99 (1970)Google Scholar
- 3.Gustafsson, B.: A numerical method for solving singular boundary value problems. Numer. Math.21, 328–344 (1973)Google Scholar
- 4.Jain, M.K., Iyengar, S.R.K., Subramanyam, G.S.S.: Variable mesh methods for the numerical solution of two point singular perturbation problems. Comput. Methods Appl. Mech. Eng.42, 273–286 (1984)Google Scholar
- 5.Jamet, P.: On the convergence of finite difference approximations to one-dimensional singular boundary value problems. Numer. Math.14, 355–378 (1970)Google Scholar
- 6.Kubíček, K., Hlaváček, V.: Numerical solution of nonlinear boundary value problems with applications. Englewood Cliffs, New Jersey: Prentice Hall 1983Google Scholar
- 7.Reddien, G.W.: Projection methods and singular two point boundary value problems. Numer. Math.21, 193–205 (1973)Google Scholar
- 8.Reddien, G.W., Schumaker, L.L.: On a collocation method for singular two point boundary value problems. Numer. Math.25, 427–432 (1976)Google Scholar
- 9.Russell, R.D., Shampine, L.F.: Numerical methods for singular boundary value problems. SIAM. J. Numer. Anal.12, 13–35 (1975)Google Scholar