Numerical Integration of Pressure Build-Up Volumes Using an L-Stable Rosenbrock Method

Simulation of fluid power systems has become a tool widely used for testing, designing and virtual prototyping. The choice of a numerical integration method for solving stiff systems of ordinary differential equations is a key factor for achieving proper stability and computational efficiency during simulation. Whereas widely used A-stable methods require small integration step sizes in order to avoid numerical oscillations when solving numerically stiff problems, the L-stable Rosenbrock method presented in this paper can take large steps. The method is implemented with an estimator of the local truncation error and a predictor of the step size. Simulations results show the good performance of the integrator in terms of both stability and efficiency.