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A numerical continuation method based on Padé approximants. (English) Zbl 0980.74021

Summary: A continuation algorithm is presented with a new predictor, which is based on a rational representation of the solution path. This algorithm belongs to the class of asymptotic numerical methods that connect perturbation techniques with a discretization principle without the use of correction process. Several examples from shell buckling and from contact mechanics are analyzed, to assess the efficiency and the reliability of the method.

MSC:

74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74G60 Bifurcation and buckling
74K25 Shells
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