On three theorems of lees for numerical treatment of semilinear two-point boundary value problems

Tetsuro Yamamoto, Shin'ichi Oishi

Research output: Contribution to journalArticle

Abstract

This paper is concerned with semilinear tow-point boundary value problems of the form -(p(x)u′)′ + f(x, u) = 0, a ≤ x ≤ b, α0u(a) - α1u′(a) = α, β1u′(b) + β,1u′(b) = β, αi ≥ 0, βi≥ 0, i = 0, 1, α01 > 0, β01 > 0, α00 > 0. Under the assumption inf fu > -λ1, where λ1 is the smallest eigenvalue of u = -(pu′)′ with the boundary conditions, unique existence theorems of solution for the continuous problem and a discretized system with not necessarily uniform nodes are given as well as error estimates. The results generalize three theorems of Lees for u″ = f(x, u), 0 ≤ x ≤ 1, u(0) = α, u(1) = β.

Original languageEnglish
Pages (from-to)293-313
Number of pages21
JournalJapan Journal of Industrial and Applied Mathematics
Volume23
Issue number3
DOIs
Publication statusPublished - 2006 Oct

Keywords

  • Discretization
  • Error estimates
  • Existence of solution
  • Theorems of Lees
  • Tow-point boundary value problems

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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