New error control methods for integration of trajectories

Track of a charged particle in a non-uniform electromagnetic field can be described by the first-order initial value problem (IVP). Robustness and efficiency of the integration process is important for overall performance of the simulation code. Geant4 and GeantV use explicit Runge-Kutta (RK) methods with the adaptive stepsize control. I propose to implement several methods which may have a better performance for the problem of interest.

• New stepsize control algorithm
• Integration methods with stable equilibrium states
• Methods especially designed for periodic problems