On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology.
Using Chawla's identity [cf. \textit{M. M. Chawla} and \textit{C. P. Katti}, SIAM J. Numer. Anal. 22, 561--565 (1985; Zbl 0578.65085)] a finite difference method based on uniform mesh is described for a class of singular boundary value problems \((p(x)y')'=p(x)f(x,y)\), \(0<x\leq 1\), \(y(0)=A\), \(\alpha y(1)+\beta y'(1)=\gamma\), or \(y'(0)=0\), \(\alpha y(1)+\beta y'(1)=\gamma\) with \(p(x)=x^{b_0}g(x)\), \(b_0\geq 0\), 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 \textit{M. M. Chawla, S. McKee} and \textit{G. Shaw} [BIT 26, 318--326 (1986; Zbl 0602.65063)] for \(p(x)=x^{b_0}\), \(b_0\geq 1\), to a general class of function \(p(x)=x^{b_0}g(x)\), \(b_0\geq 0\). Numerical examples for the general function \(p(x)\) verify the order of the convergence of the method and two physiological problems have also been solved.
two-point singular boundary value problem
scientific article; zbMATH DE number 2062752