A technique for the numerical solution of initial-value problems based on a class of Birkhoff-type interpolation method
type: Item
instance of: scholarly article
title: A technique for the numerical solution of initial-value problems based on a class of Birkhoff-type interpolation method
zbMATH Open document ID: 1268.65092
author: Mehdi Dehghan
author: S. Aryanmehr
author: M. R. Eslahchi
published in: Journal of Computational and Applied Mathematics
publication date: 2013-02-21T00:00:00Z
review text: The authors analyse various properties (construction, uniqueness, error) of a Birkhoff interpolation scheme such that a polynomial and its first \(m-1\) derivatives match a given function and corresponding derivatives at a given point, as well as the \(n\)th derivatives matching at a set of distinct nodes. This interpolation scheme is used to construct numerical methods for the general \(n\)th order initial value problem and a number of test problems (only one of which is a system) are solved.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 6138052
zbMATH Keywords: Birkhoff interpolation
zbMATH Keywords: initial value problems
zbMATH Keywords: special functions
zbMATH Keywords: quadrature rules
zbMATH Keywords: error analysis
zbMATH Keywords: numerical examples
reviewed by: Kevin Burrage
MaRDI profile type: Publication
full work available at URL: j.cam.2012.11.013
OpenAlex ID: W2066340347
DOI: 10.1016/J.CAM.2012.11.013
description: scientific article; zbMATH DE number 6138052