Mizuguchi Makoto , Takayasu Akitoshi , Kubo Takayuki , Oishi Shin'ichi , 高安 亮紀 , 久保 隆徹

This paper presents a numerical method for verifying the existence and local uniqueness of a solution for an initial-boundary value problem of semilinear parabolic equations. The main theorem of this …

SIAM journal on numerical analysis 55(2), 980-1001, 2017-04

IR 

Takayasu Akitoshi , Mizuguchi Makoto , Kubo Takayuki , Oishi Shin'ichi

RIMS Kokyuroku (1995), 122-131, 2016-04

Liu Xuefeng , Takayasu Akitoshi

Bulletin of the Japan Society for Industrial and Applied Mathematics 22(1), 67-68, 2012

J-STAGE 

Takayasu Akitoshi

Bulletin of the Japan Society for Industrial and Applied Mathematics 21(3), 227-228, 2011

J-STAGE 

OISHI Shin'ichi , TAKAYASU Akitoshi , KUBO Takayuki

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法法で,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.

IEICE technical report 110(166), 61-64, 2010-07-26

References (5)

TAKAYASU Akitoshi , OISHI Shin'ichi , KUBO Takayuki

A method of estimating operator norm of a class of linear operators is presented. This method is based on numerical computations with result verification. Then, with the use of Kantorovich's theorem f …

IEICE technical report 109(269), 45-49, 2009-11-04

References (3)