ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF INITIAL-BOUNDARY VALUE PROBLEMS FOR A DISPERSIVE HYPERBOLIC EQUATION.

Abstract

Initial-boundary value problems for an energy conserving dispersive hyperbolic equation, the Klein-Gordon equation, are considered. This equation exhibits the main feature of dispersion: The speed of propagation depends on frequency. Problems in two space dimensions with a parabolic boundary are discussed. The primary purpose of this paper is to compare the asymptotic expansion of solutions obtained by a technique we call the ray method with the asymptotic expansion of the exact solution. In the cases considered, the solutions agree. In addition a numerical comparison is made of the exact and asymptotic solutions for a specified region of space time. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1965
Accession Number
AD0619957

Entities

People

  • Norman Bleistein
  • Robert M. Lewis

Organizations

  • New York University

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Dispersions
  • Equations
  • Frequency
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space