6861
eng
reportzib
0
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2018-05-09
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Computational aspects of the Generalized Trapezoidal Rule
In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side F:IR^n -> IR^n.
When applied to such a problem, the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a non-differentiability of F. In such a situation the investigated generalized trapezoidal rule achieves a higher convergence order than the classical method. While the asymptotic behavior of the generalized method was investigated in a previous work, in the present article we develop the algorithmic structure for efficient implementation strategies
and estimate the actual computational cost of the latter.
Moreover, energy preservation of the generalized trapezoidal rule is proved for Hamiltonian systems with piecewise linear right hand side.
1438-0064
urn:nbn:de:0297-zib-68615
submitted to Optimization Methods and Software
Richard Hasenfelder
Tom Streubel
Lutz Lehmann
Manuel Radons
Tom Streubel
Christian Strohm
Andreas Griewank
ZIB-Report
18-23
eng
uncontrolled
Algorithmic Differentiation
eng
uncontrolled
Automatic Differentiation
eng
uncontrolled
Lipschitz Continuity
eng
uncontrolled
Piecewise Linearization
eng
uncontrolled
Nonsmooth
eng
uncontrolled
Trapezoidal Rule
eng
uncontrolled
Implementation
eng
uncontrolled
Computational Cost
NUMERICAL ANALYSIS
Mathematical Optimization
MODAL-GasLab
Streubel, Tom
MODAL-Gesamt
Energy Network Optimization
https://opus4.kobv.de/opus4-zib/files/6861/ODE_imp_latest.pdf