Composite group of explicit Runge-Kutta methods

Fatin Nadiah Abd Hamid; Faranak Rabiei; Fudziah Ismail

doi:10.1063/1.4952537

Composite group of explicit Runge-Kutta methods

Fatin Nadiah Abd Hamid, Faranak Rabiei, Fudziah Ismail

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

Abstract

In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived. The proposed methods are two-step in nature and have less number of function evaluations compared to the existing Runge-Kutta method. The order conditions up to order four are obtained using rooted trees and composite rule introduced by J. C Butcher. The stability regions of RK3(2) and RK4(3) methods are presented and initial value problems of first order ordinary differential equations are carried out. Numerical results are compared with existing Runge-Kutta method.

Original language	English
Title of host publication	Innovations Through Mathematical and Statistical Research
Subtitle of host publication	Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016
Editors	Siti Nur Iqmal Ibrahim, Lai Soon Lee, Md. Sohel Rana, Fong Peng Lim, Mai Zurwatul Ahlam Mohd Jaffar, Mohd Shafie Mustafa, Chuei Yee Chen
Publisher	American Institute of Physics
ISBN (Electronic)	9780735413962
DOIs	https://doi.org/10.1063/1.4952537
Publication status	Published - 2 Jun 2016
Externally published	Yes
Event	International Conference on Mathematical Sciences and Statistics 2016 - Kuala Lumpur, Malaysia Duration: 26 Jan 2016 → 28 Jan 2016 Conference number: 2nd https://aip.scitation.org/toc/apc/1739/1 (Proceedings)

Publication series

Name	AIP Conference Proceedings
Volume	1739
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Mathematical Sciences and Statistics 2016
Abbreviated title	ICMSS 2016
Country/Territory	Malaysia
City	Kuala Lumpur
Period	26/01/16 → 28/01/16
Internet address	https://aip.scitation.org/toc/apc/1739/1 (Proceedings)

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10.1063/1.4952537

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Hamid, F. N. A., Rabiei, F., & Ismail, F. (2016). Composite group of explicit Runge-Kutta methods. In S. N. I. Ibrahim, L. S. Lee, M. S. Rana, F. P. Lim, M. Z. A. Mohd Jaffar, M. S. Mustafa, & C. Y. Chen (Eds.), Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016 [020057] (AIP Conference Proceedings; Vol. 1739). American Institute of Physics. https://doi.org/10.1063/1.4952537

Hamid, Fatin Nadiah Abd ; Rabiei, Faranak ; Ismail, Fudziah. / Composite group of explicit Runge-Kutta methods. Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016. editor / Siti Nur Iqmal Ibrahim ; Lai Soon Lee ; Md. Sohel Rana ; Fong Peng Lim ; Mai Zurwatul Ahlam Mohd Jaffar ; Mohd Shafie Mustafa ; Chuei Yee Chen. American Institute of Physics, 2016. (AIP Conference Proceedings).

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title = "Composite group of explicit Runge-Kutta methods",

abstract = "In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived. The proposed methods are two-step in nature and have less number of function evaluations compared to the existing Runge-Kutta method. The order conditions up to order four are obtained using rooted trees and composite rule introduced by J. C Butcher. The stability regions of RK3(2) and RK4(3) methods are presented and initial value problems of first order ordinary differential equations are carried out. Numerical results are compared with existing Runge-Kutta method.",

author = "Hamid, {Fatin Nadiah Abd} and Faranak Rabiei and Fudziah Ismail",

note = "Publisher Copyright: {\textcopyright} 2016 Author(s). Copyright: Copyright 2016 Elsevier B.V., All rights reserved.; International Conference on Mathematical Sciences and Statistics 2016, ICMSS 2016 ; Conference date: 26-01-2016 Through 28-01-2016",

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month = jun,

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doi = "10.1063/1.4952537",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

editor = "Ibrahim, {Siti Nur Iqmal} and Lee, {Lai Soon} and Rana, {Md. Sohel} and Lim, {Fong Peng} and {Mohd Jaffar}, {Mai Zurwatul Ahlam} and Mustafa, {Mohd Shafie} and Chen, {Chuei Yee}",

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Hamid, FNA, Rabiei, F & Ismail, F 2016, Composite group of explicit Runge-Kutta methods. in SNI Ibrahim, LS Lee, MS Rana, FP Lim, MZA Mohd Jaffar, MS Mustafa & CY Chen (eds), Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016., 020057, AIP Conference Proceedings, vol. 1739, American Institute of Physics, International Conference on Mathematical Sciences and Statistics 2016, Kuala Lumpur, Malaysia, 26/01/16. https://doi.org/10.1063/1.4952537

Composite group of explicit Runge-Kutta methods. / Hamid, Fatin Nadiah Abd; Rabiei, Faranak; Ismail, Fudziah.

Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016. ed. / Siti Nur Iqmal Ibrahim; Lai Soon Lee; Md. Sohel Rana; Fong Peng Lim; Mai Zurwatul Ahlam Mohd Jaffar; Mohd Shafie Mustafa; Chuei Yee Chen. American Institute of Physics, 2016. 020057 (AIP Conference Proceedings; Vol. 1739).

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

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T1 - Composite group of explicit Runge-Kutta methods

AU - Hamid, Fatin Nadiah Abd

AU - Rabiei, Faranak

AU - Ismail, Fudziah

N1 - Conference code: 2nd

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Y1 - 2016/6/2

N2 - In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived. The proposed methods are two-step in nature and have less number of function evaluations compared to the existing Runge-Kutta method. The order conditions up to order four are obtained using rooted trees and composite rule introduced by J. C Butcher. The stability regions of RK3(2) and RK4(3) methods are presented and initial value problems of first order ordinary differential equations are carried out. Numerical results are compared with existing Runge-Kutta method.

AB - In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived. The proposed methods are two-step in nature and have less number of function evaluations compared to the existing Runge-Kutta method. The order conditions up to order four are obtained using rooted trees and composite rule introduced by J. C Butcher. The stability regions of RK3(2) and RK4(3) methods are presented and initial value problems of first order ordinary differential equations are carried out. Numerical results are compared with existing Runge-Kutta method.

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BT - Innovations Through Mathematical and Statistical Research

A2 - Ibrahim, Siti Nur Iqmal

A2 - Lee, Lai Soon

A2 - Rana, Md. Sohel

A2 - Lim, Fong Peng

A2 - Mohd Jaffar, Mai Zurwatul Ahlam

A2 - Mustafa, Mohd Shafie

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PB - American Institute of Physics

T2 - International Conference on Mathematical Sciences and Statistics 2016

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Hamid FNA, Rabiei F, Ismail F. Composite group of explicit Runge-Kutta methods. In Ibrahim SNI, Lee LS, Rana MS, Lim FP, Mohd Jaffar MZA, Mustafa MS, Chen CY, editors, Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016. American Institute of Physics. 2016. 020057. (AIP Conference Proceedings). https://doi.org/10.1063/1.4952537

Composite group of explicit Runge-Kutta methods

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