On higher-order differentiation in nonlinear mechanics

Modelling often involves nonlinear parametric problems and bifurcation analysis. This interdisciplinary paper reviews higher-order numerical methods for the solution of nonlinear problems, and proposes a synthesis of two different conceptual frameworks, namely automatic differentiation and the asymp...

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Bibliographic Details
Published in:Optimization methods & software 2012-04, Vol.27 (2), p.221-232
Main Author: Charpentier, I.
Format: Article
Language:English
Subjects:
74-02
asymptotic methods
automatic differentiation
bifurcation analysis
Diamant
Mechanics
Methods
nonlinear problems
Numerical analysis
Studies
Taylor series
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Description
Summary:Modelling often involves nonlinear parametric problems and bifurcation analysis. This interdisciplinary paper reviews higher-order numerical methods for the solution of nonlinear problems, and proposes a synthesis of two different conceptual frameworks, namely automatic differentiation and the asymptotic numerical method. Various mechanical problems and references illustrate the presentation.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2011.577775