Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation

Autor:	Griewank, Andreas, Hasenfelder, Richard, Radons, Manuel, Streubel, Tom
Rok vydání:	2017
Předmět:	Mathematics - Numerical Analysis 65L05 65L06 65L70 65L99 65P10
Druh dokumentu:	Working Paper
Popis:	In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). 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. Comment: Submitted
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1701.00745 Zobrazit plný text záznamu View this record from Arxiv