A method of error analysis for Runge-Kutta methods
type: Item
instance of: scholarly article
title: A method of error analysis for Runge-Kutta methods
zbMATH Open document ID: 0969.65078
author: G. Yu. Kulikov
published in: Computational Mathematics and Mathematical Physics
publication date: 2001-09-25T00:00:00Z
review text: The author develops a new method for controlling the integration step in Runde-Kutta methods. In contrast to the classical one, the proposed method of error analysis for the numerical solution of ordinary differential equations is based on the global error, rather than on the local one, which is more important for the accuracy of solution. It is shown that the proposed method of controlling the numerical integration step is particularly efficient as applied to implicit Runge-Kutta method. Estimates are given for numbers of iteration steps in the complete and modified Newton method that are required for a correct use of iterative approximations in the procedure of controlling the global error.
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 1472988
zbMATH Keywords: stepsize control
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: error analysis
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1472988