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J. Korean Math. Soc. 1999; 36(2): 299-316

Printed March 1, 1999

Copyright © The Korean Mathematical Society.

The convergenece of finite difference approximations for singular two-point boundary Value Problems

H. Y. Lee, J. M. Seong, and J. Y. Shin

Abstract

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We consider two finite difference approximations to a singular boundary value problem arising in the study of a nonlinear circular membrane under normal pressure. It is shown that the rates of convergence are $O(h)$ and $O(h^{2})$, respectively. An iterative scheme is introduced which converges to the solution of the finite difference equations. Finally the numerical experiments are given.

Keywords: A finite difference approximation, a singular boundary value problem, a rate of convergence

MSC numbers: 65L12, 65L10

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