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

Authors:
R. K. Pandey;Arvind K. Singh
Affiliations:
Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, India;Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, India
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

Using Chawla's 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 or y'(0) = 0, αy(1) = βy'(1) = γ with p(x) = xb0 g(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) = xb0 g(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.