Refine
Year of publication
- 2017 (1) (remove)
Document Type
- ZIB-Report (1)
Language
- English (1)
Has Fulltext
- yes (1)
Is part of the Bibliography
- no (1)
Keywords
- Automatic Differentiation (1)
- Dense Output (1)
- Energy Preservation (1)
- Lipschitz Continuity (1)
- Nonsmooth (1)
- Piecewise Linearization (1)
- Trapezoidal Rule (1)
Institute
In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:R^n \to R^n\) 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.