Co-operative research for numerical analysis and applied analysis

在1986年和1987年的两年中，我们组成了四个研究小组，研究工程、物理、生物等自然科学领域中的数学非线性现象。这些小组研究了（1）各种非线性现象的建模，（2）分析这些模型的理论方法的发展。(3)数值方法的发展;（4）为上述数值方法提供基本支持的计算算法的发展。这四个工作组在互补合作中举行了富有成效的会议，取得了许多令人感兴趣的成果。例如，我们有一个关于“建模，仿真和可视化”的研讨会。除了对应用分析和数值分析感兴趣的人外，还有许多从事流体力学、工程、等离子物理、生理学和化学等领域工作的人参加了会议，并进行了积极的讨论。我们认为，这次会议的主张提出了应用数学中一个新的分支是必要的。从理论上讲，我们为年轻的研究人员组织了“冬季研究所或数学科学”。题目是“非线性现象、理论和应用”和“计算数学的世界”。我确认，这些研究所给予重大影响的与会者在理解我们应该做什么新的应用数学。此外，我们的小组在应用数学方面取得了许多重要成果。其中一部分发表在日本应用数学杂志上。

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.