Co-operative Research on Computational Mathematics and Applied Analysis

这项合作研究旨在研究现代科学和工程中可能出现的非线性现象及其数学结构。为此，两个互补的方法-数值和分析的都是重要的。在这方面，数值方法的研究在本研究计划中也是很有意义的。反应扩散系统中的模式形成，非线性系统中的分叉现象及其数值方法，数值奇异问题及其稳定性理论，混沌与分形，自由边界问题，数值反问题，塑性与数值分析，拟阵理论，非协调有限元方法，非线性方程的迭代方法，非线性最优化问题等。在上面列出的许多主题中，已经发展了新的思想和理论。(For详情请参阅我们的研究报告）。另一个重要的主题是通过数值模拟获得的结果的“可视化”，例如，3-三维流动，反应和扩散介质中的图案形成过程，混沌和分形的“图案”等等。

This co-operative research aims to study nonlinear phenomena and their mathematical structures which may appear in modern science and engineering. For this, two complementary approaches - numerical and analytical ones are both important. In this respect, the study of numerical methods is also significant in this research program.The main topics are listed in the following. Pattern formations in reaction-diffusion systems, bifurcation phenomena in nonlinear systems and their numerical methods, singularly problems with numerical and their stability theory, chaos and fractals, free boundary problems, inverse problems with numerical methods, plasticity and numerical analysis, matroid theory, non-conforming finite element methods, iterative methods for nonlinear equations, nonlinear optimization problems and so on. New ideas and theory have been developed in a number of topics listed above. (For details, see our Research Report.)One of other important subjects is "Visualization" of results obtained by numerical simulations for e.g., 3-dimensional flows, pattern formation processes in reacting and diffusing media, "patterns" of chaos and fractals, and etc.