Tuning Runge-Kutta parameters on a family of ordinary differential equations Online publication date: Wed, 03-Jan-2018
by Charles Audet
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 8, No. 3, 2018
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.
Online publication date: Wed, 03-Jan-2018
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