Tuning Runge-Kutta parameters on a family of ordinary differential equations. (2018)

• Record Type: Journal Article
• Authors: Audet, Charles
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 8:Number 3(2018)
• Page Start: 277
• Page End: 286
• Publication Date: 2018
• Subjects: Runge-Kutta -- parameter tuning -- blackbox optimisation -- direct-search; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

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.