Towards Improved Error Estimates for Higher Order Time Integration of ODEs with Non-Smooth Right Hand Side

The classical convergence analysis of higher order ODE time integration methods is based on rather strong smoothness assumptions on the right hand side that are typically not satisfied in technical applications since spline approximations of input functions and look-up tables result in frequent discontinuities in derivatives of the right hand side. Practical experience shows, however, that nevertheless the resulting non-smooth model equations may often be solved efficiently by higher order ODE time integration methods. For one typical problem class, the present paper gives a theoretical explanation of this behaviour. The results of the theoretical analysis are illustrated by a series of numerical tests for the simplified model of an agricultural device that moves along a track being defined by the spline approximation of a periodic smooth input function.