Discrete Least Squares Approximations for Ordinary Differential Equations.

Abstract

The application of the least squares method, using C to the power q piecewise polynomials of order k + m, K > or = m, q > or = m, for obtaining approximations to an isolated solution of a nonlinear m-th order ordinary differential equation, involves integrals which in practice need to be discretized. Using for this latter purpose the k-point Gaussian quadrature rule in each subinterval, the discrete least squares schemes obtained are close to collocation, on the same points, by piecewise polynomials from C to the power M-1.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1976
Accession Number
ADA031968

Entities

People

  • Uri Ascher

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Boundary Layer
  • Boundary Value Problems
  • Continuity
  • Convergence
  • Differential Equations
  • Equations
  • Errors
  • Gaussian Quadrature
  • Integrals
  • Iterations
  • Least Squares Method
  • Mathematics
  • Partial Differential Equations
  • Plastic Explosives
  • Polynomials
  • United States

Fields of Study

  • Mathematics

Readers

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