非線形楕円型偏微分方程式の精度保証法

摘要

This report is concerned with numerical verification methods for solutions to Drichlet boundary value problems of semilinear elliptic equations. There are two existing methods on this type of computer assisted proofs. Proposed method is another method of computer assisted proof for the existence of solutions. Based on New ton-Kantorovich theorem, verification conditions can be derived by a pure analytic way. A computational cost of the established method is several (up to 10) times more than that of the approximation. An illustrative result with respect to the performance is presented.%本報告では非線形楕円型偏微分方程式のDrichlet境界値問題の解に対する精度保証付き数値計算方法について述べる.提案手法は先行研究とは違うまったく新しい精度保証方法で，Newton-Kantorovichの定理に基づき，自然に精度保証条件が導かれる.さらにこの手法は近似解計算の数倍程度の手間で精度保証可能である．精度保証付き数値計算法の計算速度について効果的な結果を得ることができた．