Global Error Control in the Runge-Kutta Solution of a Hamiltonian System using the RKQ Algorithm

TL;DR

This paper demonstrates the effectiveness of the RKQ algorithm in controlling global error during the numerical solution of Hamiltonian systems, highlighting its advantages even with explicit Runge-Kutta methods.

Contribution

The study applies the RKQ algorithm to Hamiltonian systems, showing its capability to control both local and global errors stepwise, regardless of using explicit methods.

Findings

RKQ effectively controls global error in Hamiltonian systems

Explicit Runge-Kutta methods can be used successfully with RKQ

Good error control results demonstrated on test problems

Abstract

We study the effect of global error control in the numerical solution of Hamiltonian systems. In particular, we apply the RKQ algorithm in the numerical solution of a Hamiltonian system. This algorithm is designed to provide stepwise control of both local and global error. A test problem demonstrates the error control features of RKQ. Good results are obtained, despite the fact that explicit Runge-Kutta methods have been used in RKQ, rather than symplectic Runge-Kutta methods. This simply emphasizes the value of stepwise global error control, as per the RKQ algorithm.