Accession Number : AD0672929

Title :   AN APPLICATION OF A NEWTON-LIKE METHOD TO THE EULER-LAGRANGE EQUATION,

Corporate Author : CALIFORNIA UNIV LOS ANGELES

Personal Author(s) : Tapia,Richard A.

Report Date : 1968

Pagination or Media Count : 20

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)

Descriptors :   (*FUNCTIONAL ANALYSIS, INTEGRAL EQUATIONS), (*CALCULUS OF VARIATIONS, NUMERICAL METHODS AND PROCEDURES), BANACH SPACE, SEQUENCES(MATHEMATICS), OPERATORS(MATHEMATICS), ITERATIONS, CONVERGENCE, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE