An Expansion Technique for Rendering the WKBJ Method Uniformly Valid.

Abstract

A method is proposed for obtaining a uniformly valid approximation to the solution of the wave equation in a stratified medium. The method differs from those previously used in that it is not based on ordinary asymptotic expansions but employs a multiple scale approach together with matched asymptotic expansions. The method represents an advance over conventional methods in permitting its range of validity to include transition points. It also, in principle, lends itslef particularly well to iteration. For illustration the procedure has been applied to the barrier transmission problem and the problem of trapped wave modes in a SOFAR channel. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 15, 1971
Accession Number
AD0742465

Entities

People

  • Vetle R. Lauvstad

Organizations

  • SACLANT ASW Research Centre

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Differential Equations
  • Equations
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Transitions
  • Wave Equations

Readers

  • Systems Analysis and Design
  • Wave Propagation and Nonlinear Chaotic Dynamics.