A mathematical theory for numerical treatment of nonlinear two-point boundary value problems

Tetsuro Yamamoto*, Shin'ichi Oishi

*この研究の対応する著者

研究成果: Article査読

6 被引用数 (Scopus)

抄録

This paper gives a unified mathematical theory for numerical treatment of two-point boundary value problems of the form -(p(x)u′)′ + f(x,u,u′)=0, a ≤ x ≤ b, α0u(a) - α1u′(a) = α, β0u(b) + β1u′(b) = β, α0, α1, β0, β10, α0 + α1 > 0, β0 + β1 > 0, α0 + β0 > 0. Firstly, a unique existence of solution is shown with the use of the Schauder fixed point theorem, which improves Keller's result [6]. Next, a new discrete boundary value problem with arbitrary nodes is proposed. The unique existence of solution for the problem is also proved by using the Brouwer theorem, which extends some results in Keller [6] and Ortega-Rheinboldt [10]. Furthermore, it is shown that, under some assumptions on p and f, the solution for the discrete problem has the second order accuracy O(h2), where h denotes the maximum mesh size. Finally, observations are given.

本文言語English
ページ(範囲)31-62
ページ数32
ジャーナルJapan Journal of Industrial and Applied Mathematics
23
1
DOI
出版ステータスPublished - 2006 2月

ASJC Scopus subject areas

  • 工学一般
  • 応用数学

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