Approximation and Bounds for Eigenvalues of Various Domains Using the Intermediate Problem Technique,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1972
- Accession Number
- AD0756672
Entities
People
- Richard E. Dame
Organizations
- The Catholic University of America