A 'Sinc-Galerkin' Method of Solution of Boundary Value Problems.

Abstract

This paper illustrates the application of a Sinc-Galerkin method to the approximate solution of linear and nonlinear second order ordinary differential equations, and to the approximate solution of some linear elliptic and parabolic partial differential equations in the plane. The method is based on approximating functions and their derivatives by use of the Whittaker cardinal function. The DE is reduced to a system of algebraic equations via new accurate explicit approximations of the inner products, the evaluation of which does not require any numerical integration. Using n function evaluations the error in the final approximation to the solution of the DE is 0 < exp (-c(n to the 1/2 d power)) > where c is independent of n, and d denotes the dimension of the region on which the DE is defined. This rate of convergence is optimal in the class of n-point methods which assume that the solution is analytic in the interior of the interval, and which ignore possible singularities of the solution at the end-points of the interval. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1977
Accession Number
ADA050662

Entities

People

  • Frank Stenger

Organizations

  • University of Utah

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Equations
  • Error Analysis
  • Errors
  • Finite Element Analysis
  • Formulas (Mathematics)
  • Fourier Series
  • Galerkin Method
  • Integral Equations
  • Intervals
  • Linear Differential Equations
  • Mathematics
  • Partial Differential Equations
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.