On the convergence of a fourth-order method for a class of singular boundary value problems

Abstract

In the present paper we extend the fourth order method developed by Chawla et al. [M.M. Chawla, R. Subramanian, H.L. Sathi, A fourth order method for a singular two-point boundary value problem, BIT 28 (1988) 88-97] to a class of singular boundary value problems (p (x) y′)′ = p (x) f (x, y), 0 < x ≤ 1y′ (0) = 0, α y (1) + β y′ (1) = γ where p (x) = xb0 q (x), b0 ≥ 0 is a non-negative function. The order of accuracy of the method is established under quite general conditions on f (x, y) and is also verified by one example. The oxygen diffusion problem in a spherical cell and a nonlinear heat conduction model of a human head are presented as illustrative examples. For these examples, the results are in good agreement with existing ones. © 2008 Elsevier B.V. All rights reserved.