Evolutionary Optimization of Runge-Kutta Coefficients for Specific Differential Equations

Abstract

Methods of numerical integration in the Runge-Kutta family are parametrized by several arrays of coefficients used in the integration process. These coefficients can take any value and still form a valid integration method, so long as they are properly normalized. This makes them well-suited to optimization by evolutionary algorithms. A program named deltaRK is introduced which uses an evolutionary algorithm to produce an integrator specialized for simulating a single differential equation. deltaRK currently only supports differential equations with an associated conserved quantity such as energy or angular momentum. Integrators produced by deltaRK are more accurate on the trained system than standard Runge-Kutta integrators with no loss in speed.