An efficient approach to the numerical verification for solutions of elliptic differential equations with local uniqueness

• Watanabe Yoshitaka

  Computing and Communications Center, Kyushu University

• Yamamoto Nobito

  Department of Computer Science and Information Mathematics, The University of Electro-Communications

• Nakao Mitsuhiro

  Faculty of Mathematics, Kyushu University

Bibliographic Information

Other Title

• 楕円型方程式の解に対する局所一意性付き数値的検証法の効率化
• ダエンガタ ホウテイシキ ノ カイ ニ タイスル キョクショ イチイセイ ツキ スウチテキ ケンショウホウ ノ コウリツカ

Abstract

One of the authors have proposed a method to prove the existence and the local uniqueness of solutions to infinite-dimensional fixed-point equations using computer. However, for second-order elliptic boundary value problems, in the case the equation includes the first-order term, it turned out that there is a possibility that the verification algorithm come to an end unsuccessfully. The purpose of this paper is to propose an alternative method to overcome this difficulity. Numerical examples compared with the previous algorithm confirm the effectiveness of the new method.

Journal

• Transactions of the Japan Society for Industrial and Applied Mathematics

  Transactions of the Japan Society for Industrial and Applied Mathematics 15 (4), 509-520, 2005

  The Japan Society for Industrial and Applied Mathematics

Details

• CRID: 1390001205767826688
• NII Article ID: 110002976854
• NII Book ID: AN10367166
• ISSN: 09172246
• ISSN: 24240982
• DOI: 10.11540/jsiamt.15.4_509
• NDL BIB ID: 7785528
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7785528
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed