# Integrating Lipschitzian dynamical systems using piecewise algorithmic differentiation

@article{Griewank2017IntegratingLD, title={Integrating Lipschitzian dynamical systems using piecewise algorithmic differentiation}, author={Andreas Griewank and Richard Hasenfelder and Manuel Radons and Lutz Lehmann and Thomas Streubel}, journal={Optimization Methods and Software}, year={2017}, volume={33}, pages={1089 - 1107} }

In this article we analyse a generalized trapezoidal rule for initial value problems with piecewise smooth right-hand side 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…

## 9 Citations

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