Project/Area Number  10440031 
Research Category 
GrantinAid for Scientific Research (B).

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  KYUSHU UNIVERSITY 
Principal Investigator 
KANAO Maitsuhiro Kyushu University, Graduate school of Mathematics, Proffesor, 大学院・数理学研究科, 教授 (10136418)

CoInvestigator(Kenkyūbuntansha) 
YAMAMOTO Tetsuro Ehime University, Mathematics, Professor, 理学部, 教授 (80034560)
MITSUI Taketomo Nagoya University, Human Informatics, Professor, 大学院・人間情報学研究科, 教授 (50027380)
MUROTA Kazuo Kyoto University, Res. Inst. Math. Sci., Professor, 数理解析研究所, 教授 (50134466)
NISHIDA Takaaki Kyoto University, Mathematics, Professor, 大学院・理学研究科, 教授 (70026110)
OISHI shin'ichi Waseda University, Informatics, Professor, 理工学部, 教授 (20139512)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥11,900,000 (Direct Cost : ¥11,900,000)
Fiscal Year 1999 : ¥5,600,000 (Direct Cost : ¥5,600,000)
Fiscal Year 1998 : ¥6,300,000 (Direct Cost : ¥6,300,000)

Keywords  Numerical analysis / Validated numerical computation / Numerical verification method / Computer assisted proof / 数値解析 / 精度保証付き数値計算法 / 解の数値的検証 / 計算機援用証明 
Research Abstract 
In this research, we extended and improved the selfvalidating numerical methods which can be applied to wide mathematical and analytical problems as well as to particular problems such as equations in the mathematical fluid mechanics. The important research results done by investigators and coinvestigators are as follows : 1. (by Nakao, N. Yamamoto and Watanabe) Several refinements and extensions were established for the numerical verification methods of solutions for elliptic problems. Namely, the numerical computation with guaranteed error bounds for the eigenvalue problems of second order elliptic operator was established by using the techniques in the numerical verification method of solutions for nonlinear elliptic boundary value problems. We also formulated and obtained basic results for the selfvalidating method for solutions of elliptic variational inequalities,. Moreover, we presented a verified computation of solutions for the NavierStokes equation based on the a posterior
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i and constructive a priori error estimates for the finite element solutions of the Stokes problems. Additionally, we computed a turning point with rigorous error bound for the perturbed and parameterized Gelfand equation. 2. (by Oishi) Some fast algorithms for the fundamental validated computations and the solutions of linear and nonlinear problems were presented. 3. (by Kikuchi) Theoretical and numerical results were obtained for the error analysis of a special kind of finite element method for electromagnetic problems. 4. (by Sakai) Some applications of splines were presented for plane data approximation. 5. (by Fujino) An efficient acceleration method was investigated for parallel machines. 6. (by Mitsui) A selfvalidating method for ordinary differential equations with initial value problems was presented. 7. (by T. Yamamoto) Some new error analysis was carried out for the ShortleyWeller type deference scheme for Dirichlet Problems. 8. (by Tabata) Several error estimates were derived of the finite element method for the problem in fluid mechanics. 9. (by Nishida) Some bifurcation phenomena in fluid dynamics were analyzed by the computer assisted proof. 10. (by Murota) The reliability in the structural engineering was investigated by using the group theoretic bifurcation arguments. 3.西田は流体方程式系の解空間の構造を解析するために、計算機援用証明法の研究開発を進めた。 4.室田は構造工学の分野における計算の信頼性に関し、群論的分岐理論を用いた考察を行った。 Less
