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Solutions of general second order ODEs using direct block method of Runge-Kutta type


Mukhtar, Nur Zahidah and Abdul Majid, Zanariah and Ismail, Fudziah and Suleiman, Mohamed (2011) Solutions of general second order ODEs using direct block method of Runge-Kutta type. Journal of Quality Measurement and Analysis, 7 (2). pp. 145-154. ISSN 1823-5670


This paper presents a three point block variable step size method of Runge-Kutta type for solving general second order ordinary differential equations (ODEs). The block method is formulated using Lagrange interpolation polynomial. Most of the mathematical problems which involve higher order ODEs could be reduced to system of first order equations. The proposed method obtains the numerical solutions directly without reducing to first order systems of ODEs. The method is used to compute the solutions at three points simultaneously by integrating the coefficients over the closest point in the block. The stability region of the block method is also studied. The numerical results obtained shows that the proposed method is more efficient compared to existing block methods in terms of total steps and execution time.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Universiti Kebangsaan Malaysia
Keywords: Block method; Variable step size; Ordinary differential equations
Depositing User: Nur Farahin Ramli
Date Deposited: 15 Jul 2013 03:50
Last Modified: 05 Apr 2017 08:41
URI: http://psasir.upm.edu.my/id/eprint/25207
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