1994 Fiscal Year Final Research Report Summary
Comprehensive Study on Fundamental and Applied Numerical Algorithms
| Project/Area Number |
04302008
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
MITSUI Taketomo Nagoya University, Graduate School of Human Informatics, Professor, 大学院・人間情報学研究科, 教授 (50027380)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Masatake University of Tokyo, Department of Applied Physics, Professor, 工学部, 教授 (20010936)
MUROTA Kazuo Kyoto University, Research Institute for Mathematical Science, Professor, 数理解析研究所, 教授 (50134466)
NAKASHIMA Masaharu Kagoshima University, Department of Mathematics, Professor, 理学部, 教授 (40041230)
TANABE Kunio Institute of Mathematical Statistics, Division on Prediction and Optimization, P, 教授 (50000203)
SHINOHARA Yoshitane Tokushima University, Faculty of Engineering, Professor, 工学部, 教授 (40035803)
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| Project Period (FY) |
1992 – 1994
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| Keywords | numerical algorithm / numerical solution of differential equations / linear system of equations / free boundary-value problem / interval arithmetic / mathematical modelling / 数理モデリング |
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| Research Abstract |
The project has some specified topics to attain its goal. Detailed research results is to be published as a report in Japanese. Summary of several main research topics is as follows :
1.Development od fast as well as large-scale algorithms for evolution equations, and analyzes of finite-difference and finite-element methods for fluid flow problems and shallow water problem have been carried out. The structure of the algorithms and methods has been elucidated.
An optimization algorithm for the charge distribution in the charge simulation method was found out, and, connected with the above item, a significant numerical method can be achieved for the numerical analysis of 2-dimensional problem.
Combinatorial structure analysis has been carried out together with the algorithm of its application, one of which is those for differential-algebraic equations.
Iterative solution for linear and nonlinear equations has been analyzed to result in its application to the self-validating numerical computation.
Much result has benn attained in the mathematical modelling of physical phenomena, numerical algorithms treating the Signorini-type condition or the spinoidal factorization derived from modelling, and their stability analysis.
Numerical algorithms for initial-value problems of ordinary differential equations as well as of stochastic differential equations are developed as discrete variable methods, and their stability has been much elucidated.
The research topics are so significant and promising that they are expected to continue under appropriate reseach project for further achievement, although our project attains results in much extent.
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