Stability of some continuously imbedded Runge-Kutta methods of Sarafyan
type: Item
instance of: scholarly article
title: Stability of some continuously imbedded Runge-Kutta methods of Sarafyan
zbMATH Open document ID: 0627.65086
DOI: 10.1016/0898-1221(87)90040-X
author: B. George
publication date: 1987-01-01T00:00:00Z
review text: \textit{D. Sarafyan} [Comput. Math. Appl. 10, 139-159 (1984; Zbl 0552.65056)] has developed novel explicit Runge-Kutta methods for the initial value problem: \(y'(t)=f(t,y(t))\), \(y(t_ 0)=y_ 0\). Associated with each method is an imbedded interpolating polynomial. In this paper two continuously imbedded methods are considered; it is shown that the polynomials possess the stability properties of the Runge-Kutta methods. That makes them useful for the problem of dense output and for rootfinding.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4020374
zbMATH Keywords: polynomial approximation
zbMATH Keywords: explicit Runge-Kutta methods
zbMATH Keywords: imbedded methods
zbMATH Keywords: stability
zbMATH Keywords: rootfinding
reviewed by: Antonio de Castro
MaRDI profile type: Publication
cites work: Continuous approximate solution of ordinary differential equations and their systems
cites work: A sixth-order imbedded Runge-Kutta algorithm with continuously variable weights
cites work: Stability of explicit Runge-Kutta methods
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4020374