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 - 2018
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6628
VL - 33
SP - 1089
EP - 1107
PB - Taylor & Francis
ER -