Numerical verification methods for a system of elliptic PDEs, and their software library

• Sekine Kouta

  Faculty of Information Networking for Innovation and Design, Toyo University

• Nakao Mitsuhiro T.

  Faculty of Science and Engineering, Waseda University

• Oishi Shin'ichi

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

抄録

Since the numerical verification method for solving boundary value problems for elliptic partial differential equations (PDEs) was first developed in 1988, many methods have been devised. In this paper, existing verification methods are reformulated using a convergence theorem for simplified Newton-like methods in the direct product space V_h × V_⊥ of a computable finite-dimensional space V_h and its orthogonal complement space V_⊥. Additionally, the Verified Computation for PDEs (VCP) library is provided, which is a software library written in the C++ programming language. The VCP library is introduced as a software library for numerical verification methods of solutions to PDEs. Finally, numerical examples are presented using the reformulated verification methods and VCP library.

収録刊行物

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 12 (1), 41-74, 2021

  一般社団法人 電子情報通信学会

キーワード

• Verified numerical computation
• partial differential equation
• computer-assisted proof

詳細情報

• CRID: 1391131406295326592
• NII論文ID: 130007965490
• DOI: 10.1587/nolta.12.41
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/12/1/12_41/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可