Optimal Method of Runge-Kutta of Order 5

Akpini K. A. Michael, Assui K Richard, Yoro Gozo and Bailly Bale

Journal of Mathematics Research, 2019, vol. 11, issue 1, 93-101

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.

Keywords: Runge-Kutta method; optimal; stability; estimation; error (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:11:y:2019:i:1:p:93

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