Computational aspects of the Generalized Trapezoidal Rule

Please always quote using this URN: urn:nbn:de:0297-zib-68615
  • 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.

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2023/05/09

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Metadaten
Author:Richard HasenfelderORCiD, Lutz Lehmann, Manuel RadonsORCiD, Tom StreubelORCiD, Christian StrohmORCiD, Andreas GriewankORCiD
Document Type:ZIB-Report
Tag:Algorithmic Differentiation; Automatic Differentiation; Computational Cost; Implementation; Lipschitz Continuity; Nonsmooth; Piecewise Linearization; Trapezoidal Rule
MSC-Classification:65-XX NUMERICAL ANALYSIS
Date of first Publication:2018/05/09
Series (Serial Number):ZIB-Report (18-23)
ISSN:1438-0064
Published in:submitted to Optimization Methods and Software