Numerical existence theorem for solutions of two-point boundary value problems of nonlinear differential equations

• Takayasu Akitoshi

  Graduate School of Fundamental Science and Engineering, Waseda University

• Oishi Shin'ichi

  Department of Applied Mathematics Faculty of Science and Engineering, Waseda University CREST, JST

• Kubo Takayuki

  University of Tsukuba

Abstract

In this paper, a numerical method is presented for verifying the existence and uniqueness of solutions to two-point boundary value problems of nonlinear ordinary differential equations. Taking into account every error of numerical computations such as the discretization error and the rounding error, this method also provides mathematically guaranteed error bounds between approximations obtained by numerical computations and the exact solution whose existence is proven by the numerical existence theorem, which is based on the Newton-Kantorovich theorem. Finally, illustrative numerical results are presented for showing the usefulness of the method.

Journal

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 1 (1), 105-118, 2010

  The Institute of Electronics, Information and Communication Engineers

Keywords

• Computer assisted proof
• Guaranteed error estimate
• Two-point boundary value problem
• Finite element method
• Numerical computations with result verification

Details

• CRID: 1390282680322077824
• NII Article ID: 130000908376
• DOI: 10.1587/nolta.1.105
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/1/1/1_1_105/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed