Improvement of Numerical Verification Results of Semilinear Elliptic Boundary Value Problems

DOI Open Access

Bibliographic Information

Other Title
  • 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>

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Details 詳細情報について

  • CRID
    1390001288140318464
  • NII Article ID
    130007618980
  • DOI
    10.11540/jsiamt.29.1_17
  • ISSN
    24240982
  • Text Lang
    ja
  • Data Source
    • JaLC
    • CiNii Articles
    • KAKEN
  • Abstract License Flag
    Disallowed

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