Continuous approximate solution of ordinary differential equations and their systems
type: Item
instance of: scholarly article
title: Continuous approximate solution of ordinary differential equations and their systems
zbMATH Open document ID: 0552.65056
DOI: 10.1016/0898-1221(84)90044-0
author: Diran Sarafyan
publication date: 1984-01-01T00:00:00Z
review text: The fifth-order Taylor polynomial of the solution \(y(x_ 0+th)\), \(0<t\leq 1\), \(h=step\)-size of \(y'=f(x,y)\), \(y(x_ 0)=y_ 0\), is approximated by Runge-Kutta processes obtaining polynomials of n-th order \(y^*_ n(x_ 0+th)\), \(n=1,2,3,4,5\). The polynomial \(y^*_ 4(x_ 0+th)\) provides an approximation of the fourth order at the interior points and of the fifth order at each end point. Its derivative constitutes a third order approximation of \((y(x_ 0+th))'\) for any t. The formulae are valid for systems.
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 3880024
zbMATH Keywords: polynomial approximation of solution
zbMATH Keywords: Runge-Kutta method
reviewed by: Antonio de Castro
MaRDI profile type: Publication
full work available at URL: 0898-1221(84)90044-0
OpenAlex ID: W2078202171
cites work: Q3238605
cites work: Numerical solution of ordinary differential equations
cites work: Q5607556
cites work: Q4053026
cites work: An investigation of Runge-Kutta processes, and equivalence of scalar and vector cases
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3880024