Title: Tuning Runge-Kutta parameters on a family of ordinary differential equations

Authors: Charles Audet

Addresses: GERAD and Département de mathématiques et génie industriel, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-ville, Montréal, Québec, H3C 3A7, Canada

Abstract: The Runge-Kutta class of iterative methods is designed to approximate solutions of a system of ordinary differential equations (ODE). The second-order class of Runge-Kutta methods is determined by a system of three nonlinear equations and four unknowns, and includes the modified-Euler and mid-point methods. The fourth-order class is determined by a system of eight nonlinear equations and 10 unknowns. This work formulates the question of identifying good values of these eight parameters for a given family of ODE as a blackbox optimisation problem. The objective is to determine the parameter values that minimise the overall error produced by a Runge-Kutta method on a training set of ODE. Numerical experiments are conducted using the NOMAD direct-search optimisation solver.

Keywords: Runge-Kutta; parameter tuning; blackbox optimisation; direct-search.

DOI: 10.1504/IJMMNO.2018.088992

International Journal of Mathematical Modelling and Numerical Optimisation, 2018 Vol.8 No.3, pp.277 - 286

Received: 03 Jun 2017
Accepted: 13 Aug 2017

Published online: 26 Dec 2017 *

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