Improvement of Numerical Verification Results of Semilinear Elliptic Boundary Value Problems
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- Sakai Masahiro
- Graduate School of Fundamental Science and Engineering, Waseda University
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- Tanaka Kazuaki
- Institute for Mathematical Science, Waseda University
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- Oishi Shin'ichi
- Faculty of Science and Engineering, Waseda University
Bibliographic Information
- Other Title
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- 半線形楕円型境界値問題の精度保証付き数値計算結果の改善
Description
<p>Abstract. We improve numerical verification results of semilinear elliptic problems through the verification of a certain linear problem. As a feature of the method described in this paper, the norm of the correction term of Newton’s method, which was conventionally evaluated by the product of an inverse-operator norm and the residual norm, is more precisely evaluated through numerical verification for the linear problem derived from an original problem. This not only improves error estimations of many approximate solutions but also enables us to verify low precision approximate solutions whose error bounds could not be evaluated.</p>
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 29 (1), 17-45, 2019
The Japan Society for Industrial and Applied Mathematics
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Keywords
Details 詳細情報について
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- CRID
- 1390001288140318464
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- NII Article ID
- 130007618980
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- ISSN
- 24240982
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- Text Lang
- ja
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- Data Source
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- JaLC
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed