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On the convergence of a fourth-order method for a class of singular boundary value problems. (English) Zbl 1188.65105

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.

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

Citations:

Zbl 0636.65079
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References:

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