Co-operative research for numerical analysis and applied analysis

在1986年和1987年的两年时间里，成立了4个研究小组，对工程、物理、生物等自然科学领域中的非线性现象进行数学研究。这些小组研究了(1)各种非线性现象的建模，(2)发展了分析这些模型的理论方法。(3)数值方法的发展；(4)基本支持上述数值方法的计算算法的发展。这些会议在互补合作中取得了丰硕成果，并产生了许多有趣的成果。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，许多人参加并积极讨论了哪些人在流体力学、工程学、等离子体物理学、生理学和化学领域工作。我们认为，这次会议的主张提出了一个新的分支，这将是应用数学所必需的。从理论上看，我们为年轻的研究人员组织了“冬季研究所或数学科学”。书名分别是“非线性现象、理论与应用”和“计算数学世界”。我确认，这些机构对学员理解我们应该为新的应用数学做些什么产生了重大影响。此外，我们的团队在应用数学方面取得了如此多的重要成果。其中部分研究发表在《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.