Extrapolation with Spline-Collocation Methods for Two-Point Boundary Value Problems. I. Justification and Proposals,

Abstract

Asymptotic expansions for the error in some spline interpolation schemes are used to derive asymptotic expansions for the truncation errors in some spline collocation methods for two-point boundary-value problems. This raises the possibility of using Richardson extrapolation or iterated deferred corrections to develop efficient high-order algorithms based on low-order collocation in analogy with similar codes based on low-order finite difference methods; some specific such procedures are proposed. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1974
Accession Number
AD0786228

Entities

People

  • James W. Daniel

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Asymptotic Series
  • Boundaries
  • Boundary Value Problems
  • Extrapolation
  • Interpolation
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Truncation

Fields of Study

  • Mathematics

Readers

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