High-Order Corrected Trapezoidal Rules for Singular Functions

Abstract

A group of quadrature formulae is presented applicable to both non- singular functions and functions with end-point singularities, generalizing the classical end-point corrected trapezoidal quadrature rules. We present an algorithm for the construction of very high-order end-point corrected trapezoidal rules, taking advantage of functional information outside the interval of integration. The scheme applies not only to non-singular functions, but also for a wide class of functions with monotonic singularities. Numerical experiments are presented demonstrating the practical usefulness of the new class of quadratures. Tables of quadrature weights are included for singularities of the form s(x) = log(absolute value of x), s(x) = absolute value of x to the lambda power for a variety of values of lambda.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1994
Accession Number
ADA284269

Entities

People

  • Sharad Kapur
  • Vladimir Rokhlin, Jr.

Organizations

  • Yale University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Computer Science
  • Construction
  • Convergence
  • Differential Equations
  • Equations
  • Integral Equations
  • Integrals
  • Intervals
  • Linear Algebraic Equations
  • Linear Systems
  • Numbers
  • Partial Differential Equations
  • Real Numbers
  • Signal Processing
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra