Accession Number:

AD0733220

Title:

A Comparison of Solutions of a Linear Homogeneous Self-Adjoint Differential Equation with Variable Coefficients by the Newton, Stodola and Rayleigh-Ritz Methods.

Descriptive Note:

Master's thesis,

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF

Personal Author(s):

Report Date:

1971-09-01

Pagination or Media Count:

55.0

Abstract:

Three techniques for finding the eigenvalues and eigenfunctions are investigated. A typical problem involves a linear homogeneous differential equation with variable coefficients of the form Px y double primed x P primed x y primed x omega sup 2 Mx O. The functions Px and Mx are functions which are positive, or have at most isolated zeroes on the fundamental interval O,L omega is a parameter. Appropriate end conditions are specified so that the problem is self-adjoint. The three methods are Newtons method, Stodolas method, and the Rayleigh-Ritz method. The methods are derived and a computer solution by each method is included in the paper. A second problem involving Bessels equation of order zero is solved using each method and a comparison of the eigenvalues and eigenfunctions is made with tabulated values. The results indicate that Newtons method is to be preferred usually. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE