A Comparison of Solutions of a Linear Homogeneous Self-Adjoint Differential Equation with Variable Coefficients by the Newton, Stodola and Rayleigh-Ritz Methods.
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 P(x) y double primed (x) + P primed (x) y primed (x) + omega (sup 2) M(x) = O. The functions P(x) and M(x) 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: Newton's method, Stodola's 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 Bessel's 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 Newton's method is to be preferred usually. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1971
- Accession Number
- AD0733220
Entities
People
- William Kent Terrell
Organizations
- Naval Postgraduate School