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

Abstract

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.

Journal

• Nonlinear Theory and Its Applications, IEICE

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

  The Institute of Electronics, Information and Communication Engineers

Keywords

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

Details

• CRID: 1391131406295326592
• NII Article 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
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed