ALL ROUND STUDY FOR THE NUMERICAL METHODS IN SCIENCE AND TECHNOLOGY

科学技术数值方法的全面研究

• 批准号: 02302011
• 负责人: USHIJIMA Teruo
• 金额: $ 6.4万
• 依托单位: THE UNIVERSITY OF ELECTRO-COMMUNICATIONS
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1990
• 资助国家: 日本
• 起止时间: 1990 至 1992
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02302011/
• 关键词: Non-stationary Iinear water wave problem; Convection diffusion difference scheme.; Steklov operator; Finite element approximation of electro-magnetic field problem; Mathematical model for phytoplankton and marine plants; Numerical computation with re

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

1.围绕首席研究员的联合工作取得的主要成果：(1) 线性水波问题有限元离散问题解的收敛证明和误差估计的抽象方法的发展。(2) 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.共同）。(3) 对流扩散差分格式 （与南名古屋市联合）。 （4）三阶精度的对流有限元格式（由Tabata，M.和Fujima，S.获得）。（5）外域泊松方程的有限元近似（与Yokomatsu，D.等人合作）。（6）带角域中拉普拉斯方程的数值方法（与Koyama，D.等人合作）。 2.研究人员在工作中取得的显着进展：（1）有髓神经轴突激发态传播的数学模型（由 Ikeda，T … More 获得。）。（2）线性化磁流体动力系统的特征值问题（由 Kako，T. 获得）。（3）静电场问题的有限元数值分析和引入 (4) 柯西型主值积分的自动数值积分法、使用快速傅立叶变换的奇异积分变换数值方法(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. 获得)。(6) 精度验证的数值方法（西田T.获得）。（7）超并行高速计算的实现（野木T.获得）。（8）浮游植物和营养物的数学模型（细野Y.获得）。（9）函数值重排理论的发展及其在变分问题中的应用（又野，T.获得）。 H.).(10)以半无限区间内缓减函数积分为目标的双指数型数值积分公式，Cahn-Hilliard方程的差分法(Mori, M.获得)。(11)界面反应机理的数学模型，半线性椭圆方程解的结构(Yotsutani, S.获得).3.与日本的联合年会 应用数学领域的合作研究（A）：从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.教授、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, H. 和名古屋大学的 Mitui, T.。较少的

项目成果

T.Ushijima,M.Matsuki: "Fully discrete approximation of a second order linear evolution equation related to the water wave problem" Proc.Int.Conf.on Functional Anaysis and Related Topics. (1993)

T.Ushijima、M.Matsuki：“与水波问题相关的二阶线性演化方程的完全离散近似”Proc.Int.Conf.on 泛函分析和相关主题。

T.Sakurai,T.Torii,H.Sugiura: "A high order iterative formula for simultaneous determination of zeros of a polynomial" Journal of Computational and Applied Mathematics. 38. 387-397 (1991)

T.Sakurai、T.Torii、H.Sugiura：“用于同时确定多项式零点的高阶迭代公式”计算与应用数学杂志。

園田 信吾,櫻井 鉄也,杉浦 洋,鳥居 達生: "分割統治法による多項式の数値的因数分解" 日本応用数理学会論文誌. 1. 277-290 (1991)

Shingo Sonoda、Tetsuya Sakurai、Hiroshi Sugiura、Tatsuo Torii：“通过分而治之法对多项式进行数值因式分解”日本应用数学学会汇刊 1. 277-290 (1991)。

H.Sugiura,T.Torii: "Polynomial interpolation on quasiequidistributed nodes on the unit circle" SIAM J.Numer.Anal.29. 1154-1165 (1992)

H.Sugiura，T.Torii：“单位圆上准等分布节点的多项式插值”SIAM J.Numer.Anal.29。

野木 達夫: "科学技術計算シュミレーション超並列計算機ADENA" 情報処理. 32. 377-387 (1991)

Tatsuo Nogi：“科学技术计算模拟大规模并行计算机 ADENA”信息处理。32. 377-387 (1991)