Local Piecewise Polynomial Projection Methods for an ODE which Give High-Order Convergence at Knots.

Abstract

Local projection methods which yield C(m-1) piecewise polynomials of order m+k as approximate solutions of a boundary value problem for an m(th) order ordinary differential equation are determined by the k linear functionals at which the residual error in each partition interval is required to vanish. We develop a condition on these k functionals which implies breakpoint superconvergence (of derivatives of order less than m) for the approximating piecewise polynomials. The same order of super-convergence is associated with eigenvalue problems. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1980
Accession Number
ADA089589

Entities

People

  • Blair Swartz
  • Carl R. de Boor

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Classification
  • Contracts
  • Differential Equations
  • Eigenvalues
  • Equations
  • Interpolation
  • Mathematics
  • Numerical Analysis
  • Polynomials
  • Residuals
  • Sequences
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

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