Third order accelerated Runge-Kutta Nyström method for solving second-order ordinary differential equations

Faranak Rabiei; Fudziah Ismail; Norihan Arifin; Saeid Emadi

doi:10.1007/978-3-642-25462-8_17

Third order accelerated Runge-Kutta Nyström method for solving second-order ordinary differential equations

Faranak Rabiei
, Fudziah Ismail
, Norihan Arifin
, Saeid Emadi

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

Abstract

In this paper, the explicit Accelerated Runge-Kutta Nyström (ARKN) method of order three with two stages for the numerical integration of second-order ordinary differential equations are developed. The method is two step in nature. Algebraic order conditions of the method are obtained and third order ARKN method is derived. Numerical examples are carried out to illustrate the efficiency of the proposed method compared to the existing Runge-Kutta Nyström (RKN) method.

Original language	English
Title of host publication	Informatics Engineering and Information Science - International Conference, ICIEIS 2011, Proceedings
Pages	204-209
Number of pages	6
Edition	PART 3
DOIs	https://doi.org/10.1007/978-3-642-25462-8_17
Publication status	Published - 2011
Externally published	Yes
Event	International Conference on Informatics Engineering and Information Science (ICIEIS) 2011 - Kuala Lumpur, Malaysia Duration: 14 Nov 2011 → 16 Nov 2011 https://link.springer.com/book/10.1007/978-3-642-25462-8 (Proceedings)

Publication series

Name	Communications in Computer and Information Science
Number	PART 3
Volume	253 CCIS
ISSN (Print)	1865-0929

Conference

Conference	International Conference on Informatics Engineering and Information Science (ICIEIS) 2011
Abbreviated title	ICEIS 2011
Country/Territory	Malaysia
City	Kuala Lumpur
Period	14/11/11 → 16/11/11
Internet address	https://link.springer.com/book/10.1007/978-3-642-25462-8 (Proceedings)

Keywords

Accelerated Runge-Kutta Nyström method
Order conditions
Second-order ordinary differential equations
Two step method

Access to Document

10.1007/978-3-642-25462-8_17

Cite this

Rabiei, F., Ismail, F., Arifin, N., & Emadi, S. (2011). Third order accelerated Runge-Kutta Nyström method for solving second-order ordinary differential equations. In Informatics Engineering and Information Science - International Conference, ICIEIS 2011, Proceedings (PART 3 ed., pp. 204-209). (Communications in Computer and Information Science; Vol. 253 CCIS, No. PART 3). https://doi.org/10.1007/978-3-642-25462-8_17

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title = "Third order accelerated Runge-Kutta Nystr{\"o}m method for solving second-order ordinary differential equations",

abstract = "In this paper, the explicit Accelerated Runge-Kutta Nystr{\"o}m (ARKN) method of order three with two stages for the numerical integration of second-order ordinary differential equations are developed. The method is two step in nature. Algebraic order conditions of the method are obtained and third order ARKN method is derived. Numerical examples are carried out to illustrate the efficiency of the proposed method compared to the existing Runge-Kutta Nystr{\"o}m (RKN) method.",

keywords = "Accelerated Runge-Kutta Nystr{\"o}m method, Order conditions, Second-order ordinary differential equations, Two step method",

author = "Faranak Rabiei and Fudziah Ismail and Norihan Arifin and Saeid Emadi",

note = "Copyright: Copyright 2011 Elsevier B.V., All rights reserved.; International Conference on Informatics Engineering and Information Science (ICIEIS) 2011, ICEIS 2011 ; Conference date: 14-11-2011 Through 16-11-2011",

year = "2011",

doi = "10.1007/978-3-642-25462-8\_17",

language = "English",

isbn = "9783642254611",

series = "Communications in Computer and Information Science",

number = "PART 3",

pages = "204--209",

booktitle = "Informatics Engineering and Information Science - International Conference, ICIEIS 2011, Proceedings",

edition = "PART 3",

url = "https://link.springer.com/book/10.1007/978-3-642-25462-8",

}

Rabiei, F, Ismail, F, Arifin, N & Emadi, S 2011, Third order accelerated Runge-Kutta Nyström method for solving second-order ordinary differential equations. in Informatics Engineering and Information Science - International Conference, ICIEIS 2011, Proceedings. PART 3 edn, Communications in Computer and Information Science, no. PART 3, vol. 253 CCIS, pp. 204-209, International Conference on Informatics Engineering and Information Science (ICIEIS) 2011, Kuala Lumpur, Malaysia, 14/11/11. https://doi.org/10.1007/978-3-642-25462-8_17

Third order accelerated Runge-Kutta Nyström method for solving second-order ordinary differential equations. / Rabiei, Faranak; Ismail, Fudziah; Arifin, Norihan et al.
Informatics Engineering and Information Science - International Conference, ICIEIS 2011, Proceedings. PART 3. ed. 2011. p. 204-209 (Communications in Computer and Information Science; Vol. 253 CCIS, No. PART 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

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AU - Arifin, Norihan

AU - Emadi, Saeid

PY - 2011

Y1 - 2011

N2 - In this paper, the explicit Accelerated Runge-Kutta Nyström (ARKN) method of order three with two stages for the numerical integration of second-order ordinary differential equations are developed. The method is two step in nature. Algebraic order conditions of the method are obtained and third order ARKN method is derived. Numerical examples are carried out to illustrate the efficiency of the proposed method compared to the existing Runge-Kutta Nyström (RKN) method.

AB - In this paper, the explicit Accelerated Runge-Kutta Nyström (ARKN) method of order three with two stages for the numerical integration of second-order ordinary differential equations are developed. The method is two step in nature. Algebraic order conditions of the method are obtained and third order ARKN method is derived. Numerical examples are carried out to illustrate the efficiency of the proposed method compared to the existing Runge-Kutta Nyström (RKN) method.

KW - Accelerated Runge-Kutta Nyström method

KW - Order conditions

KW - Second-order ordinary differential equations

KW - Two step method

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Rabiei F, Ismail F, Arifin N, Emadi S. Third order accelerated Runge-Kutta Nyström method for solving second-order ordinary differential equations. In Informatics Engineering and Information Science - International Conference, ICIEIS 2011, Proceedings. PART 3 ed. 2011. p. 204-209. (Communications in Computer and Information Science; PART 3). doi: 10.1007/978-3-642-25462-8_17

Third order accelerated Runge-Kutta Nyström method for solving second-order ordinary differential equations

Abstract

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Keywords

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