Implementation issues in solving nonlinear equations for two-point boundary value problems

J. R. Cash, Margaret H. Wright

Research output: Contribution to journalArticle

Abstract

Complex numerical methods often contain subproblems that are easy to state in mathematical form, but difficult to translate into software. Several algorithmic isues of this nature arise in implementing a Newton iteration scheme as part of a finite-difference method for two-point boundary value problems. We describe the practical as well as theoretical considerations behind the decisions included in the final code, with special emphasis on two "watchdog" strategies designed to improve reliability and allow early termination of the Newton iterates.

Original languageEnglish (US)
Pages (from-to)17-37
Number of pages21
JournalComputing
Volume45
Issue number1
DOIs
StatePublished - Mar 1990

Keywords

  • AMS Subject Classification: 65L10 (boundary value problems), 68N99 (mathematical software)
  • Boundary value problems
  • mathematical software
  • merit functions
  • nonlinear algebraic equations
  • watchdog strategy

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics

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