Relative Global Error Control in the RKQ Algorithm for Systems of Ordinary Differential Equations

Abstract

We generalize the RKrvQz algorithm to solve nonstiff initial-value problems in ordinary differential equations. The algorithm can now be applied to systems of nonstiff initial-value problems (IVPs) in ordinary differential equations, and both relative error and absolute error can be controlled, locally and globally. We demonstrate the algorithm by solving the simple harmonic oscillator for moderate and strict tolerances.