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Optimal Method of Runge-Kutta of Order 5

Author

Listed:
  • Akpini K. A. Michael
  • Assui K Richard
  • Yoro Gozo
  • Bailly Bale

Abstract

The Runge-Kutta method of order 5 with 6 stages requires finding a matrix A, whose coefficients must satisfy a system of nonlinear polynomial equations. Butcher found a 5-parameter family of solutions, which displays different characteristics depending on whether b2= 0 or b2, 0. This paper presents an optimal method in the case b2= 0, which is significantly better than several popular methods of order 4.

Suggested Citation

  • Akpini K. A. Michael & Assui K Richard & Yoro Gozo & Bailly Bale, 2019. "Optimal Method of Runge-Kutta of Order 5," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(1), pages 93-101, February.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:1:p:93
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    Cited by:

    1. Kim, Min Jae & Kim, Tong Seop & Flores, Robert J. & Brouwer, Jack, 2020. "Neural-network-based optimization for economic dispatch of combined heat and power systems," Applied Energy, Elsevier, vol. 265(C).

    More about this item

    Keywords

    Runge-Kutta method; optimal; stability; estimation; error;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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