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International Conference on Informatics Engineering and Information Science

ICIEIS 2011: Informatics Engineering and Information Science pp 204–209Cite as

Third Order Accelerated Runge-Kutta Nyström Method for Solving Second-Order Ordinary Differential Equations

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 253))

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.

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References

  1. Phohomsiri, P., Udwadia, F.E.: Acceleration of Runge-Kutta Integeration Schemes. Discrit. Dynamic. Nature. Soci. 2, 307–314 (2004)

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  4. Franco, J.M.: A Class of Explicit Two Step Hybrid Methods for Second Order IVP’s. J. Comput. Appl. Math. 187, 41–57 (2006)

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Author information

Authors and Affiliations

  1. Mathematics Department, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

    Faranak Rabiei, Fudziah Ismail & Norihan Arifin

  2. University of Derby, UK

    Saeid Emadi

Authors
  1. Faranak Rabiei
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  2. Fudziah Ismail
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  3. Norihan Arifin
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  4. Saeid Emadi
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Editor information

Editors and Affiliations

  1. Advanced Informatics School (UTM AIS), UTM International Campus, 54100, Kuala Lumpur, Malaysia

    Azizah Abd Manaf , Shamsul Sahibuddin , Rabiah Ahmad  & Salwani Mohd Daud , ,  & 

  2. Information Systems Department, King Saud University, Riyadh, Saudi Arabia

    Eyas El-Qawasmeh

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© 2011 Springer-Verlag Berlin Heidelberg

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Cite this paper

Rabiei, F., Ismail, F., Arifin, N., Emadi, S. (2011). Third Order Accelerated Runge-Kutta Nyström Method for Solving Second-Order Ordinary Differential Equations. In: Abd Manaf, A., Sahibuddin, S., Ahmad, R., Mohd Daud, S., El-Qawasmeh, E. (eds) Informatics Engineering and Information Science. ICIEIS 2011. Communications in Computer and Information Science, vol 253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25462-8_17

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  • DOI: https://doi.org/10.1007/978-3-642-25462-8_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25461-1

  • Online ISBN: 978-3-642-25462-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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