Numerical verification for positive solutions of Allen–Cahn equation using sub- and super-solution method

• Matsushima Yuta

  Graduate School of Fundamental Science and Engineering, Waseda University

• Tanaka Kazuaki

  Institute for Mathematical Science, Waseda University

• Oishi Shin’ichi

  Faculty of Science and Engineering, Waseda University

Abstract

This paper describes a numerical verification method for positive solutions of the Allen–Cahn equation on the basis of the sub- and super-solution method. Our application range extends to global-in-time solutions that converge or sufficiently approach to stable stationary solutions. The proposed verification method has almost the same memory requirements as the computation for obtaining an approximate solution.

Journal

• Journal of Advanced Simulation in Science and Engineering

  Journal of Advanced Simulation in Science and Engineering 7 (1), 136-150, 2020

  Japan Society for Simulation Technology

Keywords

• Allen–Cahn equation
• Numerical verification method
• Sub- and super-solution method

Details

• CRID: 1390566775139072256
• NII Article ID: 130007852293
• DOI: 10.15748/jasse.7.136
• ISSN: 21885303
• Web Site: https://www.jstage.jst.go.jp/article/jasse/7/1/7_136/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed