Co-operative research for numerical analysis and applied analysis

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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.