A simple numerical verification method for differential equations based on infinite dimensional sequential iteration

• Watanabe Yoshitaka

  Research Institute for Information Technology, Kyushu University

Abstract

This paper describes a numerical verification of solutions for infinite dimensional functional equations based on residual form and sequential iteration. Comparing with other verification procedures as typified by Newton-type iterations, the proposed algorithm can be done at low computational cost, although it needs that the formulated compact map is retractive in some neighborhood of the fixed-point to be verified. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations will be shown.

Journal

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 4 (1), 23-33, 2013

  The Institute of Electronics, Information and Communication Engineers

Keywords

• computer-assisted proof
• functional equations
• differential equations
• residual form
• sequential iteration

Details

• CRID: 1390282680322041344
• NII Article ID: 130003375410
• DOI: 10.1587/nolta.4.23
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/4/1/4_23/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed