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