Research Article Open Access

An Embedded Explicit Hybrid Method for Ordinary Differential Equations

F. Samat and F. Ismail

Abstract

Problem statement: Many differential systems that appear in practice were special second-order ordinary differential equations of the form y" = f (x, y). In the past research, there was a continuous need for methods for numerically solving these equations. Approach: This study describes the derivation and implementation of a pair of embedded explicit hybrid methods for solving non-stiff second-order ordinary differential equations y" = f (x, y). Results: It was shown that our method was more efficient than the well-known embedded pair of explicit runge-kutta-nystrom methods for solving some second-order problems. Conclusion: Our method can be considered as an alternative for the numerical solution of y" = f (x, y).

Journal of Mathematics and Statistics
Volume 8 No. 1, 2012, 32-36

DOI: https://doi.org/10.3844/jmssp.2012.32.36

Submitted On: 28 October 2011 Published On: 23 December 2011

How to Cite: Samat, F. & Ismail, F. (2012). An Embedded Explicit Hybrid Method for Ordinary Differential Equations. Journal of Mathematics and Statistics, 8(1), 32-36. https://doi.org/10.3844/jmssp.2012.32.36

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Keywords

  • Ordinary Differential Equations (ODEs)
  • Runge Kutta-Nystrom (RKN)
  • multistep methods
  • numerically solving
  • hybrid method