1997 Fiscal Year Final Research Report Summary
New Approaches to Scientific Computing and Applied Analysis
Project/Area Number 
08304018

Research Category 
GrantinAid for Scientific Research (A)

Allocation Type  Singleyear Grants 
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 > 九州大学, 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)
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 Period (FY) 
1996 – 1997

Keywords  Numerical analysis / Numerical solution of PDEs / Mathematical analysis for nonlinear phenomena / Validated computation 
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.

Research Products
(20 results)