Solution of Large Order Fourier-Bessel Equations,

Abstract

The solution of large order Fourier-Bessel equations, whose derivative is zero at the boundaries of a cylindrical geometry, is found using a series expansion method. It is clear from the partial derivation of a formula which attempts to evaluate analytically the large order Fourier-Bessel functions that problems are posed such that results can only be extracted with great difficulty. A major hurdle is the evaluation of the eigenvalues at large n. By contrast, an infinite series expansion truncated after an appropriately large number of terms provides the behavior hinted at (but not described) in the formula and utilizes a simpler approach. The evaluation of the integral is central to the method and this presents no difficulty. This work has examined the behavior of a perhaps recondite function at large orders, but it is one which is essential for correct analysis of the radial dependence of a wave function where the inner boundary of a cylindrical geometry has a finite value. Keywords: Great Britain, Wave equations, Duct flow, Axial flow compressors. (jhd)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1987
Accession Number
ADA195906

Entities

People

  • S. J. Roberts

Organizations

  • Admiralty Research Establishment

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Axial Flow
  • Axial Flow Compressors
  • Bessel Functions
  • Boundaries
  • Coefficients
  • Computer Programs
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Flow
  • Geometry
  • Infinite Series
  • Radial Velocity
  • Three Dimensional
  • Wave Equations
  • Wave Functions

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Educational Psychology