Numerical Methods for Singularities Via Sinc Functions.

Abstract

This paper summarizes the results known to date for using sinc functions composed with other functions as bases for approximations in numerical analysis. Described in this paper are methods of interpolation and approximation of functions and their derivatives, quadrature, the approximate evaluation of transforms (Hilbert, Fourier, Laplace, Hankel and Mellin) and the approximate solution of differential and integral equations. The methods have many advantages over classical methods which use polynomials as bases. In addition, all of the methods converge at an optimal rate, if singularities on the boundary of approximation are ignored. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 07, 1978
Accession Number
ADA065292

Entities

People

  • Frank Stenger

Organizations

  • University of Utah

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Space

DTIC Thesaurus Topics

  • Analytic Functions
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Formulas (Mathematics)
  • Galerkin Method
  • Integral Equations
  • Integrals
  • Interpolation
  • Inverse Problems
  • Numerical Analysis
  • Partial Differential Equations
  • Polynomials
  • Theorems
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.