Synthetical Researches on Applied Analysis and Computational Mathematics

应用分析与计算数学综合研究

• 批准号: 03302009
• 负责人: NISHIDA Takaaki
• 金额: $ 8.58万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 1992
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03302009/
• 关键词: Validated numerical analysis; Free surface waves of fluid; Finete element method; Dimension reduction method; Reaction Diffusion system; Double exponential transformation; Generating function of chaotic mapping; Newton method; 精度保証つき数値計算; 区間演算ソフト

New topics of applied analysis and computational mathematics in the wide sense are investigated with the collaboration of investigators. Research achievements are presented, discussed and evaluated in the two joint symposium on applied mathematics. Also several workshops and international conferences on selected topics are organized and partly supported by this project. These activated research communications and stimulated young mathematicians.1. The research group of head investigator obtained the following results:(1)Consolidation of the method of validated numerical computation. It gives a computer aided proof of the existence of periodic solution for the autonomous system of ordinary differential equations which depends delicately on the value of parameters. In the proof a software of interval analysis by the computer is necessary to evaluate the round-off errors at the each step of numerial computations. One software for the big computer Fujitsu M-1800 and one for Sun Workstations are completed and used in the researches.(2)Waves on the free surface of viscous fluid flowing sown on an inclined plane. A gloval in time existence theorem is obtained under appropriate conditions. Spectral analysis for the linearized system will be our next project which will require an improvement of the method of the above computer aided proof.2. Co-investigators obtained the following results:(1)Accurate error estimates for the solution of finite element method of evolution systems.(H.Fujita)(2)Analysis of structure change of the equilibrium solution over the wide range of parameter for reaction diffusion sytems by the reduction method of dimension.(M.Mimura)(3)Solution of boundary value problems by the double exponential transformation using Sine approximation.(M.Mori)(4)Approximation of a function by a generating function of a chaotic mapping.(M.Yamaguti)(5)Improvement of convergent radins of simplified Newton method.(T.Yamamoto)

研究人员的协作研究了广泛的应用分析和计算数学的新主题。在两个应用数学的联合研讨会上提出，讨论和评估了研究成就。此项目还组织了几次关于选定主题的研讨会和国际会议。这些激活的研究通信并刺激了年轻的数学家。1。负责人研究人员的研究小组获得了以下结果：（1）合并经过验证的数值计算方法。它提供了计算机的辅助证明，证明了对普通微分方程的自主系统的周期性解决方案的存在，该解决方程非常取决于参数的值。在证明中，必须通过计算机进行间隔分析的软件，以评估数字计算的每个步骤的圆形错误。一个用于大型计算机富士通M-1800的软件和一个用于日晒站的软件已完成并在研究中使用。（2）流动在倾斜平面上播种的粘性流体的自由表面上的波浪。在适当条件下获得了时间存在定理的吊顶。线性化系统的光谱分析将是我们的下一个项目，它将需要改进上述计算机辅助证明的方法2。共同评估者获得了以下结果：（1）进化系统有限元方法解决方案解决方案的准确误差估计。（H.Fujita）（2）分析平衡解的结构变化在反应扩散系统的广泛参数范围内的平衡溶液的结构变化，该参数是通过尺寸的还原解决方案（M.Mimura）（3）通过双向跨度的解决方案（3）的跨度。（3） （M.Mori）（4）通过混乱映射的生成函数近似函数。（M.yamaguti）（5）改进简化牛顿方法的收敛辐射。（T.Yamamoto）

项目成果

X. Chen & T. Yamamoto: "On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators" Computing. vol.49. 87-94 (1992)

陈X

H.Ito & L.Glass: "Theory of reentrant excitation in a ring of cordiac tissue" Physica D. 56. 84-106 (1992)

伊藤浩

H.Fujita & T.Suzuki: "Evolution Problems and the finite element nethod" Hamdbook of Numerical Analysis. 2. 789-928 (1991)

藤田

Okamoto,H.: "Degenerate 0(2)ーequivariant fifurcation equations & their application to the Taylor problem." Japan J.Indust.Appl.Math.8. 245-273 (1991)

Okamoto, H.：“简并 0(2)-等变分叉方程及其在泰勒问题中的应用。日本 J.Indust.Appl.Math.8 (1991)。”

M. Yamaguti & A. Morimoto: "Wevelet and its applications II (in Japanese)" Measurement and Control. Vol.31. 1066-1074 (1992)

M·山古蒂