ALL ROUND STUDY FOR THE NUMERICAL METHODS IN SCIENCE AND TECHNOLOGY

1.主要成果：(1)提出了线性水波问题的有限元离散问题解的收敛性证明和误差估计的抽象方法。(2)对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合著）。m)。(3)对流扩散差分格式（与Nagoya， S.联合）。(4)三阶精度的对流有限元方案（Tabata， M. and Fujima， S.）。(5)外域Poisson方程的有限元逼近（与Yokomatsu， D.等合作）。(6)带角域拉普拉斯方程的数值解法（与Koyama， D.等合著）。2.研究者工作取得显著进展：(1)有髓神经轴突兴奋状态传播的数学模型（由Ikeda， T…More .获得）。(2)线性化磁流体动力系统的本征值问题（Kako， T.）。(3)静电场问题的有限元数值分析与协变元的引入（Kikuchi， F.）。(4)柯西型主值积分的自动数值积分方法，利用快速傅立叶变换进行奇异积分变换的数值方法（由Torii， T.获得）。(5)非线性偏微分方程解的结果验证数值方法（Nakao, m.t.）。(6)具有精度验证的数值方法（Nishida， T.获得）。(7)超并行高速计算的实现（Nogi， T.）。(8)浮游植物与营养的数学模型（Hosono， Y.获得）。(9)发展了函数值重排理论及其在变分问题中的应用（由Matano， H.获得）。（10）针对半无穷区间内缓降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）。应用数学领域合作研究(A)联合年会：1990年至1992年，每年12月在京都大学举行为期3天的研讨会，由首席研究员和其他合作研究(A)的首席研究员共同组织，他们是千叶大学的Kawarada， H.，德岛大学的Shinohara， Y.，早稻田大学的Hirose， K.，东北大学的Sato， M.，九州大学的Arikawa， S.，京都大学的Nishida， T.，庆应义塾大学的Enomoto和名古屋大学的Mitui。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