Continuation of Newton’s Method Through Bifurcation Points

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1969 English Publisher:ASME InternationalJournal:Journal of Applied Mechanics, volume 36, pages 425-430 (issn: 0021-8936, eissn: 1528-9036,

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Authors: Thurston, G. A.;

doi: 10.1115/1.3564697

Continuation of Newton’s Method Through Bifurcation Points

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Abstract

A modification of Newton’s method is suggested that provides a practical means of continuing solutions of nonlinear differential equations through limit points or bifurcation points. The method is applicable when the linear “variational” equations for the problem are self-adjoint. The procedure is illustrated by examples from the field of elastic stability.

Related Organizations

Martin Marietta Materials, Inc.
United States

Keywords

Numerical computation of solutions to single equations, Numerical solution of discretized equations for boundary value problems involving PDEs

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