GENERATING BESSEL FUNCTIONS WITH AN ANALOG COMPUTER,

Abstract

Because of an indeterminate expression at the origin, Bessel functions J sub n(x) have not been amenable to an accurate generation with analog computers for 0 < x < x max. This report extends an idea of Van Remoortere to use an approximation for 0 < x < x sub 1 and solve a differential equation for x sub 1 < x < x max, combining both phases by switching. The technique described uses Chebyshev polynomials to minimize equipment in the approximation phase, and generates the function 1/x by an integration process in the differential-equation phase to extend the range. The examples given for J sub o, J sub 1, and J sub 9 indicate excellent accuracy for at least 0 < x < 100.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1966
Accession Number
AD0643144

Entities

People

  • Arthur Hausner

Organizations

  • Harry Diamond Laboratories

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Analog Computers
  • Bessel Functions
  • Chebyshev Polynomials
  • Computers
  • Demographic Cohorts
  • Differential Equations
  • Equations
  • Mathematics
  • Polynomials
  • Switching

Readers

  • Linear Algebra
  • Systems Analysis and Design
  • Theoretical Analysis.