TABLES OF EIGENVALUES OF THE WAVE EQUATION IN PROLATE SPHEROIDAL COORDINATES

Abstract

The wave equation in prolate spheroidal coordinates was separated into radial and angle functions. The differential equation satisfied by the angle functions was written in the form of an eigenvalue problem, that is, as a linear operator operating on eigenfunctions to yield the same eigenfunctions multiplied by corresponding eigenvalues. The eigenvalues were numerically calculated by use of Galerkin's method. This method reduces to the evaluation of the characteristic roots of a large matrix. An 80 by 80 matrix is chosen and a detailed calculation on a high-speed computer leads to a tabulation. The table of prolate eigenvalues published here has the range m = 0, 1, 2; l = m (1) m + 49; h = 0.1 (0.1) 0.9, 1.0 (0.2) 8.0, 10.0, 20.0 (20.0) 100.0. The precision is 21 significant figures.

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Document Details

Document Type
Technical Report
Publication Date
Apr 04, 1969
Accession Number
AD0686658

Entities

People

  • B. King
  • S. Hanish

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Acoustic Propagation
  • Acoustics
  • Computations
  • Computer Programming
  • Computers
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Helmholtz Equations
  • Liouville Equation
  • Mathematics
  • Permutations
  • Precision
  • Three Dimensional
  • Wave Equations

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra