Vol. 29, No. 1, 1969

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An application of a Newton-like method to the Euler-Lagrange equation

Richard Alfred Tapia

Vol. 29 (1969), No. 1, 235–246
Abstract

It is known that any function which minimizes a functional of the form J(y) = αbf(x,y,y) and satisfies prescribed boundary values must be a solution of the corresponding Euler-Lagrange equation: f3(x,y,y) axf2(x,y,y) = c. Let us call any equation of the form: g(x,y,y) axh(x,y,y) = c a generalized Euler-Lagrange equation.

In this paper we propose a Newton-like method and show that this proposed method is general enough to enable us to construct solutions of the generalized Euler-Lagrange equation.

Mathematical Subject Classification
Primary: 65.50
Milestones
Received: 12 February 1968
Published: 1 April 1969
Authors
Richard Alfred Tapia