On the Numerical Solution of Two-Point Boundary Value Problems

Abstract

This paper, presents a new numerical method for the solution of linear two-point boundary value problems of ordinary differential equations. After reducing the differential equation to a second kind integral equation. The latter are discretized via a high order Nystrom scheme. A somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using O(N (dot) p2) operations, where N is the number of nodes on the interval and p is the desired order of convergence. Thus, the advantages of the integral equation formulation (small condition number, insensitivity to boundary layers, insensitivity to end-point singularities, etc.) are retained, while achieving a computational efficiency previously available only to finite difference or finite element methods. Keywords: Two-Point boundary value problems; Integral equations; Chebyshev polynomials; Approximation theory.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1989
Accession Number
ADA211244

Entities

People

  • L. Greengard
  • Vladimir Rokhlin

Organizations

  • Yale University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Chebyshev Approximations
  • Chebyshev Polynomials
  • Coefficients
  • Construction
  • Convergence
  • Differential Equations
  • Equations
  • Integral Equations
  • Linear Algebraic Equations
  • Linear Systems
  • Partial Differential Equations
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)