Runge-Kutta-Nyström-Methods with Maximized Stability Domain for Stiff Mechanical Systems

Problems in structural dynamics lead quite often to stiff second order ODEs. Solving them as first order ODE with explicit methods results in very small stepsizes due to high frequency oscillations and instability. Implicit methods, on the other hand, are not well-suited for real-time applications and very large problems. Thus, there is a need for low order methods that allow relatively large steps and that are computationally not expensive. In this paper, we introduce a class of Runge-Kutta-Nystrom methods that meet the requirements above. The methods generalize the well-known Stormer’s rule and allow a maximization of the stability domain.