Project/Area Number  08304018 
Research Category 
GrantinAid for Scientific Research (A)

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

Research Institution  KYUSYU UNIVERSITY 
Principal Investigator 
NAKAO Mitsyhiro KYUSYU UNIVERSITY Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (10136418)

CoInvestigator(Kenkyūbuntansha) 
伊理 正夫 中央大学, 理工学部, 教授 (40010722)
YAMAMOTO Tetsuro Ehime University, Mathematics, professor, 理学部, 教授 (80034560)
MORI Masatake Kyoto University, Res.Inst.Math.Sci., professor, 数理解析研究所, 教授 (20010936)
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)
USHIJIMA Teruo Univ.Elec.Comm., Computer Science, Professor, 電気通信学部, 教授 (10012410)

Project Fiscal Year 
1996 – 1997

Project Status 
Completed(Fiscal Year 1997)

Budget Amount *help 
¥9,400,000 (Direct Cost : ¥9,400,000)
Fiscal Year 1997 : ¥4,500,000 (Direct Cost : ¥4,500,000)
Fiscal Year 1996 : ¥4,900,000 (Direct Cost : ¥4,900,000)

Keywords  Numerical analysis / Numerical solution of PDEs / Mathematical analysis for nonlinear phenomena / Validated computation / 数値解析 / 偏微分方程式の数値解法 / 非線形現象の数理解析 / 精度保証付き数値計算 / 科学計算 / 有限要素法 / 非線形問題 
Research Abstract 
In this research, we extended and improved the general and existing numerical methods as well as analyzed and developed some new methods for the numerical analysis for individual mathematical problems appeared in the natural phenomena. The important research results done by investigators and coinvestigators are as follows : 1. (by Nakao) Several refinements were established for the numerical verification methods of solutions for elliptic problems. And the basic formulation and some numerical results were obtained for the eigenvalue problems of second order elliptic operator. Moreover, some a posteriori and constructive a priori error estimates for the finite element solutions of the Stokes problems, which is a preliminary result for the verified computation of solutions for the NavierStokes equation. 2. (by Ishihara) The convergence analysis was done on some iterative method for nonlinear equations. 3. (by Iso) A practically efficient technique was established for the illposed problems by using the boundary element method. 4. (by Ushijima) Using Steklov operator, several results of mathematical and numerical analysis were derived for the finite element approximation of the infinite dimensional problems. 5. (by Ohtsuka) The modelization and analysis were carried out for the fracture phenomena. 6. (by Tadata) The accurate computational method for the drag and lift coefficients was obtained for the NavierStokes equations. 7. (by Mori and Sugihara) Double exponential formula was studied with application to the Sinc approximation of functions as well as several kinds of difference schemes for PDEs were analyzed. 8. (by Nishida) Some bifurcation phenomena were studied by the computer assisted proof. 9. (by Murota) The method of discrete convex analysis was established for the nonlinear optimization. 10. (by Yamamoto) Some mathematical results were established for nonlinear SOR method. 11.非線形SOR法の数学的理論を構築しその数値解法への適用を行った(山本). 12.松隈型方程式の正値解について,その漸近挙動をはじめとする解の構造を明らかにした(四ッ谷).
