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Solving Biomechanical Model Using Third-Order Runge-Kutta Methods

  • R. R. Ahmad
  • A. S. Rambely
  • L. H. Lim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5081)

Abstract

A certain biomechanical model involves ordinary differential equations. This research focuses on solving a biomechanical model of a cyclist coasting downhill. The objective of this study is to establish the velocity of the model, using two numerical methods, i.e., the third-order Runge-Kutta methods. The two methods are the existing classical Runge-Kutta and a modified Runge-Kutta method formed by Wazwaz. The numerical results obtained from these two methods are compared with the exact solution and the relative errors are produced.

Keywords

Biomechanics problem Runge-Kutta Modified Runge- Kutta 

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References

  1. 1.
    Rao, S.S.: Applied Numerical Methods for Engineers and Scientists. Prentice Hall, New Jersey (2002)Google Scholar
  2. 2.
    Nigg, B.M., Herzog, W. (eds.): Biomechanics of the Musculo-Skeletal system. John Wiley and Sons, England (2001)Google Scholar
  3. 3.
    Wazwaz, A.-M.: A Modified Third-order Runge-Kutta method. Appl. Math Letter. 3(3), 123–125 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Wolfram, S.: Mathematica: A System For Doing Mathematics By Computer,2nd edn. Addison-Wesley, Reading (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • R. R. Ahmad
    • 1
  • A. S. Rambely
    • 1
  • L. H. Lim
    • 2
  1. 1.School of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia, UKM BangiSelangorMalaysia
  2. 2.Maths DeptUniversiti Tunku Abdul Rahman, Petaling JayaSelangorMalaysia

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