Spectral Integration and Two-Point Boundary Value Problems

Abstract

A numerical method for two-point boundary value problems with constant coefficients is developed which is based on integral equations and the spectral integration matrix for Chebyshev nodes. The method is stable, achieves superalgebraic convergence, and requires O(N log N) operations, where N is the number of nodes in the discretization. Although stable spectral methods have been constructed in the past, they have generally been based on reformulating the recurrence relations obtained through spectral differentiation in an attempt to avoid the ill-conditioning introduced by that process. Keywords: Differential equations, Spectral methods, Quadrature, Chebyshev polynomials, Approximation theory, Algorithms.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1988
Accession Number
ADA199805

Entities

People

  • L. Greengard

Organizations

  • Yale University

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Chebyshev Polynomials
  • Coefficients
  • Convergence
  • Differential Equations
  • Equations
  • Errors
  • Finite Element Analysis
  • Floating Point Operations
  • Integral Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Poisson Equation

Fields of Study

  • Mathematics

Readers

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