A numerical verification method for the existence of weak solutions for nonlinear boundary value problems

Mitsuhiro T. Nakao

研究成果: Article

48 引用 (Scopus)

抜粋

In this paper, we consider a numerical technique which enables us to verify the existence of solutions for nonlinear two point boundary value problems (BVP). We formulate the problem as a fixed point of a Newton-like operator and present a verification algorithm by computer based on Sadovskii's fixed point theorem. In order to compute the Newton type iterative sequences in infinite dimensional space, two concepts, the rounding and the rounding error, are introduced. Also some numerical examples are illustrated. We emphasize that, since the present method uses the weak formulation of BVP and the finite element approximations instead of the existing validation techniques, it is aslo applicable, in principle, to the BVP for partial differential equations as it stands.

元の言語English
ページ(範囲)489-507
ページ数19
ジャーナルJournal of Mathematical Analysis and Applications
164
発行部数2
DOI
出版物ステータスPublished - 1992 3 1
外部発表Yes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

フィンガープリント A numerical verification method for the existence of weak solutions for nonlinear boundary value problems' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

  • これを引用