• DOI:10.1080/10556788.2017.1378653
• Corpus ID: 52989136

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}
}

• A. Griewank, Richard Hasenfelder, +2 authors T. Streubel
• Published 3 January 2017
• Mathematics
• Optimization Methods and Software

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. 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.