A method of computer assisted proof for nonlinear two-point boundary value problems using higher order finite elements

• Takayasu Akitoshi

  Graduate School of Fundamental Science and Engineering, Waseda University

• Oishi Shin'ichi

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

抄録

Present authors have presented with Takayuki Kubo at University of Tsukuba a method of a computer assisted proof for the existence and uniqueness of solutions to two-point boundary value problems of nonlinear ordinary differential equations in the paper submitted for NOLTA, IEICE. This method uses piecewise linear finite element base functions and sometimes requires fine mesh. To overcome this difficulty, in this paper, an improved method is presented for the norm estimation of the residual to the operator equation. In this refined formulation, piecewise quadratic finite element base functions are used. A kind of the residual technique works sophisticatedly well. It is stated that the estimation of the residual can be expected smaller than that of the previous method. Finally, four examples are presented. Each result demonstrates that a remarkable improvement is achieved in accuracy of the guaranteed error estimation.

収録刊行物

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 2 (1), 74-89, 2011

  一般社団法人 電子情報通信学会

キーワード

• computer assisted proof
• verified numerical computation
• finite element method

詳細情報

• CRID: 1390282680322918144
• NII論文ID: 130000903444
• DOI: 10.1587/nolta.2.74
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/2/1/2_1_74/_pdf
• 本文言語コード: en
• データソース種別:
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• 抄録ライセンスフラグ: 使用不可