Runge-Kutta interpolants based on values from two successive integration steps
type: Item
instance of: scholarly article
title: Runge-Kutta interpolants based on values from two successive integration steps
zbMATH Open document ID: 0695.65046
DOI: 10.1007/BF02242920
author: Ch. Tsitouras
author: George Papageorgiou
published in: Computing
publication date: 1990-01-01T00:00:00Z
review text: The explicit Runge-Kutta method is one of the most popular techniques for solving non-stiff initial value problems of the form \(y'(x)=f(x,y(x))\), \(x\geq x_ 0\), \(y\in {\mathbb{R}}^ 4\), \(y(x_ 0)=y_ 0\). To get an efficient method for problems requiring dense output, one constructs an interpolant based on sufficient number of approximations \(y_ n\) to \(y(x_ n)\), \(x_ n=x_{n-1}+h_{n-1}\), \(n\geq 1\) and the corresponding derivatives \(y'_ n.\) In the last few years several authors have been working on the idea of producing interpolants for Runge-Kutta methods. The authors of the present note deal with the construction of various new interpolants based on values of the solution and its derivative from two successive integration steps. They also make contributions to quantify the effect of variable step size on the magnitude of the error of the constructed interpolants. There are numerical tests for the efficiency of the authors' results.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4139218
zbMATH Keywords: explicit Runge-Kutta method
zbMATH Keywords: non-stiff initial value problems
zbMATH Keywords: interpolants
zbMATH Keywords: variable step size
zbMATH Keywords: numerical tests
reviewed by: Hans Ade
describes a project that uses: dverk
describes a project that uses: nag
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02242920
OpenAlex ID: W114660188
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description: scientific article; zbMATH DE number 4139218