A family of numerical methods for the solution of high-order general initial value problems
type: Item
instance of: scholarly article
title: A family of numerical methods for the solution of high-order general initial value problems
zbMATH Open document ID: 0619.65056
DOI: 10.1016/0045-7825(88)90066-7
author: E. H. Twizell
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: A family of numerical methods is developed for the solution of the general initial value problem \(y^{(N)}(t)=f(t,y,y',...,y^{(N-1)})\), \(t>t_ 0\), with \(y(t_ 0)\), \(y^{(r)}(t_ 0)\) given \((r=1,2,...,N- 1)\). The orders of the methods are seen to be one or two and global extrapolation is used to increase the order of a given method by one or two powers. The methods are tested on the Blasius nonlinear third-order initial value problem and on a linear fourth-order problem from ship dynamics.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4005479
zbMATH Keywords: global extrapolation
zbMATH Keywords: Blasius nonlinear third-order initial value problem
zbMATH Keywords: linear fourth-order problem
zbMATH Keywords: ship dynamics
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90066-7
OpenAlex ID: W1988220345
cites work: Q5674335
description: scientific article; zbMATH DE number 4005479