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On higher-order differentiation in nonlinear mechanics. (English) Zbl 1242.41031

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.

MSC:

41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
65P30 Numerical bifurcation problems
68N19 Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.)
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
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