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

Richard Alfred Tapia

Vol. 29 (1969), No. 1, 235–246

DOI: 10.2140/pjm.1969.29.235

Abstract

It is known that any function which minimizes a functional of the form J(y) = ∫ _α^bf(x,y,y′) and satisfies prescribed boundary values must be a solution of the corresponding Euler-Lagrange equation: f₃(x,y,y′) −∫ _a^xf₂(x,y,y′) = c. Let us call any equation of the form: g(x,y,y′) −∫ _a^xh(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