Continuation of Newton’s Method Through Bifurcation Points

[+] Author and Article Information
G. A. Thurston

Martin Marietta Corporation, Denver, Colo.

J. Appl. Mech 36(3), 425-430 (Sep 01, 1969) (6 pages) doi:10.1115/1.3564697 History: Received February 11, 1969; Online September 14, 2011


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.

Copyright © 1969 by ASME
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