ALL ROUND STUDY FOR THE NUMERICAL METHODS IN SCIENCE AND TECHNOLOGY

1.主要成果：（1）发展了线性水波问题有限元离散化问题解的收敛性证明和误差估计的抽象方法。(2)关于线性水波特征值问题近似问题解的全局收敛性的考虑（与Matsuki. M.）。(3)对流-扩散差分格式（与名古屋，S.合著）。(4)三阶精度的对流有限元格式（由Tabata，M.和Fujima，S.）。(5)外区域上Poisson方程的有限元逼近（与Yokomatsu，D.和其他）。(6)本文讨论了角点区域上的拉普拉斯方程的数值解法。和其他）。2.研究者在工作中取得的显著进展：（1）有髓神经轴突兴奋状态传播的数学模型（由Ikeda，T ...更多信息 .). (2)线性化磁流体动力学系统的特征值问题（由Kako，T.获得）。(3)静电场问题的有限元数值分析以及适用于该问题的协变元素的介绍（由菊池，F.获得）。(4)柯西型主值积分的自动数值积分方法，奇异积分变换的快速傅立叶变换数值方法（由Torii，T.获得）。(5)非线性偏微分方程（Nakao，M. T.）。(6)具有精度验证的数值方法（由Nishida，T.获得）。(7)实现超并行高速计算（由Nogi，T.获得）。(8)浮游植物和营养物的数学模型（由Hosono，Y.获得）。(9)发展的理论重新安排的价值观的职能和它的应用变分问题（获得的Matano，H.）。(10)半无限区间内弱减函数积分的双指数型数值积分公式，Cahn-Hilliard方程的差分法（Mori，M.）(11)界面反应机理的数学模型，半线性椭圆方程解的结构（由Yotsutani，S.获得）。3.与应用数学领域合作研究（A）的联合年会：从1990年到1992年，每年12月在京都大学举行为期3天的研讨会，由其他合作研究（A）的首席研究员和首席研究员共同组织，他们是Kawarada，H.的千叶大学，Shinohara，Y.的德岛大学，广濑，K。早稻田大学的Sato，M.东北大学的有川，S. Nishida，T.日本京都大学的Enomoto，H.和Mitui，T.是名古屋大学的。少

1.Main Results Obtained in the joint Works around the Head lnvestigator :(1) Development of an abstract method for the convergence proof and the error estimate for the solutions of the finite element discretized problem of the linear water wave problem.(2) Consideration on the global convergence property of the solutions of the approximate problems for the linear water wave eigen-value problem (jointly with Matsuki. M.).(3) Convection-Diffusion difference scheme (jointly with Nagoya, S.). (4) Convection finite element scheme with the 3rd order accuracy (obtained by Tabata, M. and Fujima, S.).(5) Finite element approximation for the Poisson equation in an exterior domain (Jointly with Yokomatsu, D. and others).(6) Numerical method for the Laplace equation in a domain with corner (jointly with Koyama, D. and others). 2.Remarkable Progress Obtained in the Works by Investigators:(1) Mathematical model for the propagation of the excited state of myelinated nerve axsons (obtained by Ikeda, T … More .).(2) Eigen-value problem for the linearized magneto-hydrodynamic system (obtained by Kako, T.).(3) Finite element numerical analysis for electro- static field problems and introduction of the covariant elements fitted to the problems (obtained by Kikuchi, F.).(4) Automatic numerical integration method for the principal value integral of Cauchy type, Numerical method for singular integral transformation using fast Fourier transformation (obtained by Torii, T.).(5) Result verification numerical method for the solutions of nonlinear partial differential equations (obtained by Nakao, M. T.).(6) Numerical method with accuracy verification (obtained by Nishida, T.).(7) Actualization of super parallel high speed computation (obtained by Nogi, T.).(8) Mathematical model for phytoplankton and nutriment (obtained by Hosono, Y.).(9) Development of a theory for the rearrangement of the values of functions and its application to variational problems (obtained by Matano, H.).(10) Numerical integration formula of double exponential type aimed at the integration of mildly decreasing function in the half infinite interval, Difference method for Cahn-Hilliard equation (obtained by Mori, M.).(11) Mathematical model for interfacial reaction mechanism, structure of the solutions of semilinear elliptic equations (obtained by Yotsutani, S.).3.Joint Annual Meetings with Co-operative Researches (A) in the Field of Applied Mathematics:Every December from 1990 to 1992, a 3-days symposium was held at Kyoto University, co-organized by the head investigator and head investigators of other Co-operative Researches (A), who are Professors Kawarada, H. of Chiba University, Shinohara, Y. of Tokushima University, Hirose, K. of Waseda University, Sato, M. of Tohoku University, Arikawa, S. of Kyusyu University, Nishida, T. of Kyoto University, Enomoto, H. of Keio University, and Mitui, T. of Nagoya University. Less