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Accelerated Runge-Kutta Methods
Joint Authors
Udwadia, Firdaus E.
Farahani, Artin
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-38, 38 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-09-16
Country of Publication
Egypt
No. of Pages
38
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Udwadia, Firdaus E.& Farahani, Artin. 2008. Accelerated Runge-Kutta Methods. Discrete Dynamics in Nature and Society،Vol. 2008, no. 2008, pp.1-38.
https://search.emarefa.net/detail/BIM-498314
Modern Language Association (MLA)
Udwadia, Firdaus E.& Farahani, Artin. Accelerated Runge-Kutta Methods. Discrete Dynamics in Nature and Society No. 2008 (2008), pp.1-38.
https://search.emarefa.net/detail/BIM-498314
American Medical Association (AMA)
Udwadia, Firdaus E.& Farahani, Artin. Accelerated Runge-Kutta Methods. Discrete Dynamics in Nature and Society. 2008. Vol. 2008, no. 2008, pp.1-38.
https://search.emarefa.net/detail/BIM-498314
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-498314