Accession Number : AD0756672

Title :   Approximation and Bounds for Eigenvalues of Various Domains Using the Intermediate Problem Technique,

Corporate Author : CATHOLIC UNIV OF AMERICA WASHINGTON D C INST OF OCEAN SCIENCE AND ENGINEERING

Personal Author(s) : Dame,Richard E.

Report Date : JUN 1972

Pagination or Media Count : 130

Abstract : A variational method was developed to obtain lower bounds for eigenvalues, eigenfunctions and general solutions to problems which have complicated boundary conditions or regional shapes. By using an intermediate-problem approach, field functions were expanded in a infinite Fourier type expansion in a Hilbert space of eigenfunctions of a conveniently related problem. Final solutions are developed by projecting the field function into a subspace which is orthogonal to a given infinite dimensional subspace of constraints. The purpose of the study is to develop a new method which could generate the difficult eigenfunctions and boundary-value problem solutions, since previous investigators have universally limited their developments of the intermediate problem method to eigenvalue determinations. The results of this study, therefore, show that solutions of difficult problems which were not accessible through other means can now be generated efficiently. (Author)

Descriptors :   (*BOUNDARY VALUE PROBLEMS, *APPROXIMATION(MATHEMATICS)), MATRICES(MATHEMATICS), DIFFERENCE EQUATIONS, PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS, VIBRATION, MEMBRANES, LOADS(FORCES), GRAPHICS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE