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C 1 ‐continuous time integration based on cubic Hermite interpolation
Author(s) -
Mergel Janine C.,
Sauer Roger A.,
OberBlöbaum Sina
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610365
Subject(s) - monotone cubic interpolation , piecewise , hermite interpolation , hermite polynomials , mathematics , interpolation (computer graphics) , cubic hermite spline , convergence (economics) , integrator , rate of convergence , cubic function , scheme (mathematics) , order (exchange) , mathematical analysis , computer science , physics , linear interpolation , polynomial interpolation , bicubic interpolation , key (lock) , classical mechanics , motion (physics) , computer network , computer security , bandwidth (computing) , finance , economics , polynomial , economic growth
We discuss a C 1 ‐continuous time integration method based on piecewise cubic Hermite approximation. This method, denoted as p2‐scheme, belongs to a class of one‐step integration methods derived recently [1]. It exhibits a convergence rate of order four and shows properties similar to variational integrators, such as an excellent long‐term energy preservation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)