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

抄録

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.

収録刊行物

• 日本シミュレーション学会英文誌

  日本シミュレーション学会英文誌 7 (1), 136-150, 2020

  一般社団法人 日本シミュレーション学会

キーワード

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

詳細情報

• CRID: 1390566775139072256
• NII論文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
• 本文言語コード: en
• データソース種別:
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