On higher-order differentiation in nonlinear mechanics

Abstract

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.

Keywords:

• nonlinear problems
• bifurcation analysis
• Taylor series
• asymptotic methods
• automatic differentiation
• Diamant

2000 Mathematics Subject Classifications :

• 41A58
• 65P30
• 68N19
• 74-02

Acknowledgements

The author gratefully acknowledges A. Griewank for his advice and warm encouragement on several aspects of AD.