A Finite-difference Method for a Class of Singular Two-point Boundary-value Problems
- 1 October 1984
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis
- Vol. 4 (4) , 457-466
- https://doi.org/10.1093/imanum/4.4.457
Abstract
We consider a three-point finite-difference method for the singular two-point boundary-value problem: y+ (2/x)y' + f(x, y) = 0, 0 < x ≰ 1, y'(0) = 0, y(l) = a, obtained by replacing y' and y by the simplest central difference approximations. The resulting method is simpler than the classical three-point discretization of the problem. Our purpose in the present paper is to study the O(h2)-convergence of the resulting finite difference discretizations and the solution of the non-linear difference equations by Newton's method; these results are illustrated by two examples.Keywords
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