The Numerical Evaluation of a Certain Integral with a Rapidly Oscillating Integrand.

Abstract

This Memorandum considers the numerical evaluation of integrals of the form 'over the range from 0 to t, the integral: e(to the alpha times S power), times sin 2W(sub 0)S, times the -3/2 power of the quantity (d squared + the square of (Y(sub 0)-VS)), times ds' by two methods. The first is conventional. The second is unconventional and exploits the possibility of expanding the expression 'd(squared) + (Y(sub 0)-VS)(Squared)' in terms of Legendre polynomials. The integrals whose evaluation is discussed, arose in the study of the following problem. A sinusoidal source, with strength that falls off as the inverse cube of the distance from the source, moves in a straight line past a receiver with velocity much smaller than the field propagation velocity.

Document Details

Document Type
Technical Report
Publication Date
Mar 15, 1970
Accession Number
AD0870495

Entities

People

  • Brian W. Conolly
  • Hans R. Krol

Organizations

  • SACLANT ASW Research Centre

Tags

DTIC Thesaurus Topics

  • Integrals
  • Mathematics
  • Polynomials
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering