A Comparison of Solutions of a Linear Homogeneous Self-Adjoint Differential Equation with Variable Coefficients by the Newton, Stodola and Rayleigh-Ritz Methods.
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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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
- Theoretical Mathematics