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Co-operative research for numerical analysis and applied analysis

数值分析和应用分析的合作研究

基本信息

批准号：
61302008
负责人：
MIMURA Masayasu
金额：
$ 6.72万
依托单位：
HIROSHIMA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1986
资助国家：
日本
起止时间：
1986 至 1987
项目状态：
已结题

项目摘要

For two years of 1986 and 1987, 4 research groups have been formed to study mathematically nonlinear phenomena in natural sciences such as engineering, physics, biology and other fields. The groups have studied (1) modeling of a variety of nonlinear phenomena, (2) development of theoretical methods to analysis such models. (3) development of numerical methods, and (4) development of computational algorithms which basically support the above numerical metthods. These froups have fruitful meetings in complementary cooperation with each other and have produced a lot of interesting results. For instance, we had a workshop on "Modeling, Simulation & Visualization". In addition to the people who are interested in applied analysis and numerical analysis, so many people participated and actively discussed who worked in the fields of fluid dynamics, engineering, plasma physis, physiology and chemistry.We believe that the claim of this meeting suggest a new branch which will be necessary in applied mathematics.From a theoretical viewpoint, we organized the "Winter Institute or Matheamtical Science" for young researchers. The titles are "Nonlinear phenomena, theories and applications" and the "The world of computational mathematics". I confirm that these institutes give a significant influence on the attendants in understanding what should we do for new applied mathematics. Also, our groups have produced so many important results in applied mathematics. Parts of these are published in Japan Journal of Applied Mahtematics.

1986年和1987年两年，成立了4个研究组，研究工程、物理、生物学等自然科学领域的数学非线性现象。这些小组研究了（1）各种非线性现象的建模，（2）开发分析此类模型的理论方法。 (3)数值方法的发展，以及(4)基本支持上述数值方法的计算算法的发展。这些小组进行了富有成效的会议，优势互补，产生了很多有趣的成果。例如，我们举办了一个关于“建模、模拟和可视化”的研讨会。除了对应用分析和数值分析感兴趣的人之外，还有许多在流体动力学、工程学、等离子体物理学、生理学和化学领域工作的人参加并积极讨论。我们相信这次会议的主张提出了应用数学中必要的一个新分支。从理论角度来看，我们为年轻研究人员组织了“冬季研究所或数学科学”。标题是“非线性现象、理论和应用”和“计算数学的世界”。我确信这些机构对与会者理解我们应该为新应用数学做什么有重大影响。此外，我们的小组在应用数学方面取得了许多重要成果。其中部分内容发表在《日本应用数学杂志》上。