Numerov's method for a class of nonlinear multipoint boundary value problems
type: Item
instance of: scholarly article
title: Numerov's method for a class of nonlinear multipoint boundary value problems
zbMATH Open document ID: 1264.65115
DOI: 10.1155/2012/316852
author: Yuan-Ming Wang
author: Wen-Jia Wu
author: Massimo Scalia
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We give a numerical treatment for a class of nonlinear multipoint boundary value problems. The multipoint boundary condition under consideration includes various commonly discussed boundary conditions, such as the three- or four-point boundary condition. The problems are discretized by the fourth-order Numerov's method. The existence and uniqueness of the numerical solution are investigated by the method of upper and lower solutions. The convergence and the fourth-order accuracy of the method are proved. An accelerated monotone iterative algorithm with the quadratic rate of convergence is developed for solving the resulting nonlinear discrete problems. Some applications and numerical results are given to demonstrate the high efficiency of the approach.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 6173182
Wikidata QID: Q58911424
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/316852
OpenAlex ID: W2001201881
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description: scientific article; zbMATH DE number 6173182