Co-operative Research on Computational Mathematics and Applied Analysis

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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.