AN APPLICATION OF A NEWTON-LIKE METHOD TO THE EULER-LAGRANGE EQUATION,
Abstract
It is known that any function which minimizes a functional of the form J(y) = the integral taken from a to b, of f(x,y,y') and satisfies prescribed boundary values must be a solution of the corresponding Euler-Lagrange equation: f sub 3(x,y,y') - (the integral taken from a to x of f sub 2(x,y,y')) = c. Let us call any equation of the form: g(x,y,y') - (the integral taken from a to x of h(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. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1968
- Accession Number
- AD0672929
Entities
People
- Richard A. Tapia
Organizations
- University of California, Los Angeles