Formulas and Tables of Coefficients for Numerical Differentiation with Function Values Given at Unequally Spaced Points and Application to Solution of Partial Differential Equations

Abstract

General differentiation formulas for successive derivatives of a function are obtained in terms of the values of the function at unequally spaced arguments and the corresponding distances between the successive arguments using Lagrangian polynomials of various degrees. The remainder term is also obtained. Tables of coefficients in the formulas for the first four derivatives are given in intervals of 0.01 for the special case where only one spacing at either and is different from the others, as is often encountered near a curved boundary, for different ratios of this spacing to the others.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1950
Accession Number
ADA381892

Entities

People

  • Chung-hua Wu

Organizations

  • National Aeronautics and Space Administration

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Difference Equations
  • Differential Equations
  • Engineering
  • Equations
  • Flow
  • Fluid Flow
  • Grids
  • Nonlinear Differential Equations
  • Partial Differential Equations
  • Subsonic Flow
  • Thermal Stresses
  • Turbine Blades

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Operations Research
  • Regression Analysis.

Technology Areas

  • Space
  • Space - Space Objects