TY - JOUR A1 - Griewank, Andreas A1 - Hasenfelder, Richard A1 - Radons, Manuel A1 - Lehmann, Lutz A1 - Streubel, Tom T1 - Integrating Lipschitzian dynamical systems using piecewise algorithmic differentiation T2 - Optimization Methods and Software N2 - In this article we analyse a generalized trapezoidal rule for initial value problems with piecewise smooth right-hand side F : IR^n -> IR^n based on a generalization of algorithmic differentiation. When applied to such a problem, the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a nondifferentiability of F. The advantage of the proposed generalized trapezoidal rule is threefold: Firstly, we can achieve a higher convergence order than with the classical method. Moreover, the method is energy preserving for piecewise linear Hamiltonian systems. Finally, in analogy to the classical case we derive a third-order interpolation polynomial for the numerical trajectory. In the smooth case, the generalized rule reduces to the classical one. Hence, it is a proper extension of the classical theory. An error estimator is given and numerical results are presented. Y1 - 2017 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6628 VL - 33 SP - 1089 EP - 1107 PB - Taylor & Francis ER -