6628
2018
2018
eng
1089
1107
33
article
Taylor & Francis
0
2017-10-03
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Integrating Lipschitzian dynamical systems using piecewise algorithmic differentiation
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.
Optimization Methods and Software
10.1080/10556788.2017.1378653
yes
urn:nbn:de:0297-zib-64639
Andreas Griewank
Tom Streubel
Richard Hasenfelder
Manuel Radons
Lutz Lehmann
Tom Streubel
Mathematical Optimization
MODAL-GasLab
Streubel, Tom
MODAL-Gesamt
Energy Network Optimization