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A Three-Stage Multiderivative Explicit Runge-Kutta Method

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DOI: 10.4236/ajcm.2013.32020    3,902 Downloads   6,691 Views   Citations

ABSTRACT

In recent years, the derivation of Runge-Kutta methods with higher derivatives has been on the increase. In this paper, we present a new class of three stage Runge-Kutta method with first and second derivatives. The consistency and stability of the method is analyzed. Numerical examples with excellent results are shown to verify the accuracy of the proposed method compared with some existing methods.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Wusu, M. Akanbi and S. Okunuga, "A Three-Stage Multiderivative Explicit Runge-Kutta Method," American Journal of Computational Mathematics, Vol. 3 No. 2, 2013, pp. 121-126. doi: 10.4236/ajcm.2013.32020.

References

[1] M. A. Akanbi and S. A. Okunuga, “On Region of Absolute Stability and Convergence of 3-Stage Multiderivative Explicit Runge-Kutta Methods,” Journal of the Sciencea Research and Development Institute, Vol. 10, 2005-2006, pp. 83-100.
[2] M. A. Akanbi, S. A. Okunuga and A. B. Sofoluwe, “Error Bounds for 2-Stage Multiderivative Explicit Runge-Kutta Methods,” Advances in Modelling and Analysis, Vol. 45, No. 2, 2008, pp. 57-72.
[3] D. Goeken and O. Johnson, “Fifth-Order Runge-Kutta with Higher Order Derivative Approximations,” Electronic Journal of Differential Equations, Vol. 2, 1999, pp. 1-9.
[4] M. A. Akanbi, “On 3-Stage Geometric Explicit Runge-Kutta Method for Singular Autonomous Initial Value Problems in Ordinary Differential Equations,” Computing, Vol. 92, No. 3, 2011, pp. 243-263. doi:10.1007/s00607-010-0139-3
[5] J. C. Butcher, “Numerical Methods for Ordinary Differential Equations in the 20th Century,” Journal of Computational and Applied Mathematics, Vol. 125, No. 1-2, 2000, pp. 1-29. doi:10.1016/S0377-0427(00)00455-6
[6] J. C. Butcher, “Numerical Methods for Ordinary Differential Equations,” John Wiley & Sons Ltd., Chichester, 2003. doi:10.1002/0470868279
[7] S. O. Fatunla, “Numerical Methods for IVPs in ODEs,” Academic Press Inc., New York, 1988.
[8] A. S. Wusu, S. A. Okunuga and A. B. Sofoluwe, “A Third-Order Harmonic Explicit Runge-Kutta Method for Autonomous Initial Value Problems,” Global Journal of Pure & Applied Mathematics, Vol. 8, No. 4, 2012, pp. 441-451.
[9] J. D. Lambert, “Computational Methods in ODEs,” John Wiley & Sons, New York, 1973.
[10] J. D. Lambert, “Numerical Methods for Ordinary Differential Systems: The Initial Value Problem,” John Wiley & Sons, London, 1991.
[11] J. H. J. Lee, “Numerical Methods for Ordinary Differential Systems: A Survey of Some Standard Methods,” M.Sc. Thesis, University of Auckland, Auckland, 2004.

  
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