Volume 1 Number 3 (Nov. 2011)
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IJAPM 2011 Vol.1(3): 191-194 ISSN:2010-362X
DOI: 10.7763/IJAPM.2011.V1.37

Third-Order Improved Runge-Kutta Method for Solving Ordinary Differential Equation

Faranak Rabiei and Fudziah Ismail

Abstract—In this paper we constructed the sets of explicit third-order Improved Runge-Kutta (IRK) methods. The method used in two and three stage which indicated as the required number of function evaluations per step. The third-order IRK method in two-stage has a lower number of function evaluations than the classical third-order RK method while maintaining the same order of local accuracy. In three-stages, the new method is more accurate compared to the classical third-order RK method. The stability region of methods are given and numerical examples are presented to illustrate the efficiency and accuracy of the new methods.

Index Terms—Improved Runge-Kutta Methods, two-step runge-kutta methods, order conditions, stability region, ordinary differential equations.

Faranak Rabiei is with the Department of Mathematics, Faculty of Science, University Putra Malaysia (email: rabiei@math.upm.edu.my)

 

Cite: Faranak Rabiei and Fudziah Ismail, "Third-Order Improved Runge-Kutta Method for Solving Ordinary Differential Equation," International Journal of Applied Physics and Mathematics  vol. 1, no. 3, pp. 191-194, 2011.

General Information

ISSN: 2010-362X
Frequency: Bimonthly (2011-2014); Quarterly (Since 2015)
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca
Abstracting/ Indexing: Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Electronic Journals Library, Engineering & Technology Digital Library, Nanowerk Database, Google Scholar and ProQuest
E-mail: ijapm@iap.org
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