NUMERICAL DIFFERENTIATION USING ORTHOGONAL POLYNOMIAL

Abstract

The present method of reducing data by formulating a polynomial, taking the derivative and substituting experimental values, has been simplified for instances where the independent variable is evenly spaced and the derivative is desired at these given points only. Orthogonal polynomials, resembling Legendre polynomials, are differentiated and tabulated in a useful form. When used in conjunction with available orthogonal polynomial tables, these new tables give derivatives more readily than the usual procedure. These tables present coefficients for obtaining first derivatives at 6 to 21 evenly spaced points. This report extends the available orthogonal polynomial tables to sixth and seventh degrees, when appropriate, and gives a demonstration of the method.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1967
Accession Number
AD0663363

Entities

People

  • George H. Jonas

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Ballistics
  • Classification
  • Coefficients
  • Construction
  • Intervals
  • Maryland
  • New Jersey
  • Polynomials
  • Security
  • Terminal Ballistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Electrical Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space
  • Space - Orbital Debris