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

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 ≤ 1 y ′ ( 0 ) = 0 , α y ( 1 ) + β y ′ ( 1 ) = γ where p ( x ) = x b 0 q ( x ) , b 0 ≥ 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.