APPLICATION OF THE GALERKIN METHOD TO SELFADJOINT, NON-POSITIVE DEFINITE EIGENVALUE PROBLEMS IN HYDRODYNAMIC STABILITY,

Abstract

The method of Galerkin for obtaining approximate eigenvalues is applied to a class of self-adjoint but not positive definite (M-definite) eigenvalue problems. The present investigation shows that the positive and negative approximate eigenvalues obtained from the Galerkin method are respectively the upper and lower bounds of the corresponding exact eigenvalues. It is also shown that the sequence of approximate eigenvalues obtained using successively more expansion functions converges monotonically to the exact eigenvalues. Finally a method for predetermining the signs of the approximate eigenvalues is given. As numerical examples of the theory, two M-definite eigenvalue problems arising from inviscid stability analyses of flows between concentric cylindrical surfaces are cnsidered. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 25, 1964
Accession Number
AD0601107

Entities

People

  • Sherman Tsao

Organizations

  • Rensselaer Polytechnic Institute

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Eigenvalues
  • Equations
  • Galerkin Method
  • Mathematical Analysis
  • Mathematics
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Linear Algebra