On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology

Using Chawlaʹs identity (BIT 29 (1989) 566) a finite difference method based on uniform mesh is described for a class of singular boundary value problems (p(x)y′)′=p(x)f(x,y), 0<x⩽1,y(0)=A, αy(1)+βy′(1)=γ,ory′(0)=0, αy(1)+βy′(1)=γwith p(x)=xb0g(x), b0⩾0, and it is shown that the method is of second-order accuracy under quite general conditions on p(x) and f(x,y). This work also extends the method developed by Chawla et al. (BIT 26 (1986) 326) for p(x)=xb0, b0⩾1, to a general class of function p(x)=xb0g(x), b0⩾0. Numerical examples for general function p(x) verify the order of the convergence of the method and two physiological problems have also been solved.