A Comparison of Numerical Integration Methods With a View to Fast Simulation of Mechanical Dynamical Systems

Abstract

Mechanical dynamical systems, as they occur for instance in machine dynamics and robotics, often give rise to systems of moderately stiff ordinary differential equations. In this paper it will be shown that one of the most widely used classes of integration methods, multistep methods with variable step size and order, is not always optimal, especially not for systems with small damping. The classical fourth-order Runge-Kutta method has a small advantage in this case and methods that exploit the second-order structure of the equations of motion again have an advantage over these.

Implicit integration methods, which allow of a larger step size than explicit methods, but require more work for each step, will be compared to the given explicit integration methods. The Runge-Kutta-Rosenbrock methods, a class of so-called semi-implicit methods, appear to be superior in efficiency to fully implicit methods such as the Gauss-Legendre methods or the Newmark method, notwithstanding the weaker stability properties.