Approximation of the solution of certain nonlinear ODEs with linear complexity
type: Item
instance of: scholarly article
title: Approximation of the solution of certain nonlinear ODEs with linear complexity
zbMATH Open document ID: 1186.65100
author: Ezequiel Dratman
published in: Journal of Computational and Applied Mathematics
publication date: 2010-02-12T00:00:00Z
review text: This paper deals with a finite difference method for the approximation of semilinear elliptic problems in one dimension subject to nonlinear Neumann boundary conditions. The main result provides an algorithm which computes an \(\varepsilon-\)approximation of a positive solution for the semilinear problem. Such an algorithm relies on the homotopy continuation method. It is also proved that the cost of the algorithm is linear in terms of the number of nodes involved in the discretization.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 5669159
zbMATH Keywords: Two-point boundary problem
zbMATH Keywords: Finite differences
zbMATH Keywords: Neumann boundary condition
zbMATH Keywords: homotopy continuation
zbMATH Keywords: complexity
zbMATH Keywords: algorithm
zbMATH Keywords: positive solution
zbMATH Keywords: semilinear problem
MaRDI profile type: Publication
full work available at URL: j.cam.2009.10.019
OpenAlex ID: W1978358527
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DOI: 10.1016/J.CAM.2009.10.019
description: scientific article; zbMATH DE number 5669159