Pandey, R. K.; Singh, Arvind K. On the convergence of a fourth-order method for a class of singular boundary value problems. (English) Zbl 1188.65105 J. Comput. Appl. Math. 224, No. 2, 734-742 (2009). Summary: In the present paper we extend the fourth order method developed by [M. M. Chawla, R. Subramanian and H. L. Sathi, BIT 28, No. 1, 88–97 (1988; Zbl 0636.65079)] to a class of singular boundary value problems\[ \begin{aligned} & (p(x)y')'=p(x)f(x,y),\quad 0<x\leq 1\\ & y'(0)=),\quad \alpha y(1)+\beta y'(1)=\gamma\end{aligned} \]where \(p(x)=x^{b_0}q(x)\), \(b_0\geq 0\) 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. Cited in 16 Documents MSC: 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65L12 Finite difference and finite volume methods for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations Keywords:two point singular boundary value problems; finite difference method; Chawla’s identity; numerical examples; numerical examples; fourth order method; oxygen diffusion problem; nonlinear heat conduction Citations:Zbl 0636.65079 PDFBibTeX XMLCite \textit{R. K. Pandey} and \textit{A. K. Singh}, J. Comput. Appl. Math. 224, No. 2, 734--742 (2009; Zbl 1188.65105) Full Text: DOI References: [1] Adam, J. A., A mathematical model of tumor growth II: Effects of geometry and spatial nonuniformity on stability, Math. Biosci., 86, 183-211 (1987) · Zbl 0634.92002 [2] Adam, J. 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