Discretization principles for linear two-point boundary value problems, III

Tetsuro Yamamoto, Shin'Ichi Oishi, M. Zuhair Nashed, Zi Cai Li, Qing Fang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper extends results of Yamamoto et al. (Numer. Funct. Anal. Optimiz. 2008; 29:213-224) to the boundary value problem [image omitted] where the sign of r(x) is indefinite. Let HνAνUν= fν be the finite difference equations on partitions [image omitted], =1,2, with [image omitted] as , where Hν and A ν are diagonal and tridiagonal matrices, respectively, and f ν are vectors generated by discretization of f(x). Then equivalent conditions for the boundary value problem to have a unique solution u ∈ C2[a, b] are given in terms of [image omitted] and [image omitted].

Original languageEnglish
Pages (from-to)1180-1200
Number of pages21
JournalNumerical Functional Analysis and Optimization
Volume29
Issue number9-10
DOIs
Publication statusPublished - 2008 Sep 1

Keywords

  • Discretization principles
  • Finite difference methods
  • Two-point boundary value problems

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

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