Approximate Expansion for Function Theoretic Representation of Solutions of the Helmholtz Equation

Abstract

This document is based on a presentation given at the American Mathematical Society National Meeting, New Orleans, Louisiana, January 1986. We start from a function theoretic (transmutation) representation of the solutions of the class of Helmholtz equations that have coefficients that vary in one direction and satisfy a radiation condition in orthogonal directions. The kernal of the required transmutation operator satisfies a mixed Cauchy-Gorsat problem for a hyperbolic partial differential equation in two variables. We present an expansion of the kernal function that can be truncated to produce approximations that are suitable for applications for the desired transmutations, and we compare to other approximation techniques.

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Document Details

Document Type
Technical Report
Publication Date
Aug 03, 1987
Accession Number
ADA227339

Entities

People

  • David H. Wood
  • Mark D. Duston
  • Robert P. Gilbert

Organizations

  • Lehigh University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Acoustics
  • Boundaries
  • Coefficients
  • Continents
  • Differential Equations
  • Equations
  • Fourier Series
  • Geographic Regions
  • Helmholtz Equations
  • Kernel Functions
  • North America
  • Partial Differential Equations
  • Perturbation Theory
  • Perturbations
  • Power Series
  • Refractive Index
  • Underwater Acoustics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Clinical Trial Research.