THE DIFFERENCE CORRECTION METHOD FOR NON-LINEAR TWO-POINT BOUNDARY VALUE PROBLEMS,

Abstract

The numerical solution of non-linear two-point boundary value problems is discussed. It is shown that for a certain class of finite difference approximations the a posteriori use of a difference correction raises the order of the approximation by at least two orders. The difference correction itself involves only the solution of one system of linear equations. If Newton's method is used in the early stage, then it is shown that the matrices in both processes are identical, which is a useful feature in coding the method for an automatic computer. Several numerical examples are given. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 25, 1965
Accession Number
AD0612478

Entities

People

  • Victor Pereyra

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Automatic
  • Boundaries
  • Boundary Value Problems
  • Computer Programming
  • Computers
  • Computing-Related Activities
  • Differential Equations
  • Equations
  • Mathematics
  • Software Development

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis