Composite group of explicit Runge-Kutta methods

Fatin Nadiah Abd Hamid, Faranak Rabiei, Fudziah Ismail

Research output: Chapter in Book/Report/Conference proceedingConference PaperOther


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 languageEnglish
Title of host publicationInnovations Through Mathematical and Statistical Research
Subtitle of host publicationProceedings of the 2nd International Conference on Mathematical Sciences and Statistics, ICMSS 2016
EditorsSiti Nur Iqmal Ibrahim, Lai Soon Lee, Md. Sohel Rana, Fong Peng Lim, Mai Zurwatul Ahlam Mohd Jaffar, Mohd Shafie Mustafa, Chuei Yee Chen
PublisherAmerican Institute of Physics
ISBN (Electronic)9780735413962
Publication statusPublished - 2 Jun 2016
Externally publishedYes
EventInternational Conference on Mathematical Sciences and Statistics 2016 - Kuala Lumpur, Malaysia
Duration: 26 Jan 201628 Jan 2016
Conference number: 2nd (Proceedings)

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


ConferenceInternational Conference on Mathematical Sciences and Statistics 2016
Abbreviated titleICMSS 2016
CityKuala Lumpur
Internet address

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