Accelerated Runge-Kutta methods
type: Item
instance of: scholarly article
title: Accelerated Runge-Kutta methods
zbMATH Open document ID: 1152.65081
DOI: 10.1155/2008/790619
author: Artin Farahani
author: Firdaus E. Udwadia
published in: Discrete Dynamics in Nature and Society
publication date: 2008-10-16T00:00:00Z
full work available at URL: https://eudml.org/doc/129484
review text: Summary: Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, we propose a set of simple, explicit, and constant step-size accerelated-Runge-Kutta methods that are two-step in nature. For orders 3, 4, and 5, they require only 2, 3, and 5 function evaluations per time step, respectively. Therefore, they are more computationally efficient at achieving the same order of local accuracy. We present here the derivation and optimization of these accelerated integration methods. We include the proof of convergence and stability under certain conditions as well as stability regions for finite step sizes. Several numerical examples are provided to illustrate the accuracy, stability, and efficiency of the proposed methods in comparison with standard Runge-Kutta methods.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 5352079
MaRDI profile type: Publication
OpenAlex ID: W1963831470
Wikidata QID: Q58644535
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description: scientific article; zbMATH DE number 5352079