The method of quasilinearization and a three-point boundary value problem

Author(s)

Paul W. Eloe, University of DaytonFollow
Yang Gao, University of Dayton

Document Type

Article

Publication Date

2002

Publication Source

Journal of the Korean Mathematical Society

Abstract

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green's function is constructed. For nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

Inclusive pages

319-330

ISBN/ISSN

0304-9914

Document Version

Published Version

Comments

This document is made available in compliance with the publisher's policy on self-archiving or with the express permission of the publisher. Permission documentation is on file.

Volume

39

Issue

2

Peer Reviewed

yes

eCommons Citation

Eloe, Paul W. and Gao, Yang, "The method of quasilinearization and a three-point boundary value problem" (2002). Mathematics Faculty Publications. 114.
https://ecommons.udayton.edu/mth_fac_pub/114