Nonlinear Analysis by Numerical Verification Methods
数值验证方法的非线性分析
基本信息
- 批准号:13640105
- 负责人:
- 金额:$ 1.6万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2001
- 资助国家:日本
- 起止时间:2001 至 2002
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The objects of this research are partial differential equations (PDEs) with free boundaries. In 2001, we treated problems defined on the unit square in R^2. As the free boundaries are defined by potential contour which is obtained through some eigenvalue problem, we developed techniques of verified computation for eigenpairs of eigenvalue problems on partial differential operators. In these techniques, we adopted spectrum methods for approximation and error estimationIn order to treat other shapes of domains than the unit square, we improved existing verification methods to PDEs on nonconvex polygonal domains and obtained a more simple and accurate methodIn 2002, we developed a methods of verified computation for PDEs defined on annuli. Using specrum method based on Fourier-Bessel functions, we needed coefficients of Bessel expansion with guaranteed accuracy. The coefficients are defined through an eigenvalue problem concerning a one-dimensional PDE with two points boundary valuesWe developed methods for verification of existence and nonexistence of eigenvalues in order to obtain the validated values of the coefficients. The method for nonexistence is simpler and more effective than existing methods, which we have shown by numerical calculationsMoreover, a software package to calculate the values of Bessel functions with guaranteed accuracy has been developed. It is constructed on INTLAB which is a library for interval calculation with verified computation on MATLAB
本文的研究对象是具有自由边界的偏微分方程。在2001年,我们处理了定义在R^2中单位平方上的问题。由于自由边界是由特征值问题得到的位势轮廓定义的,我们发展了偏微分算子特征值问题特征对的验证计算技术.为了处理单位正方形以外的其他形状的区域,我们改进了现有的非凸多边形区域上偏微分方程的验证方法,得到了一种更简单、更精确的方法。利用基于Fourier-Bessel函数的谱方法,需要保证精度的Bessel展开系数。11系数是通过一维两点边值偏微分方程的特征值问题来定义的,为了得到系数的有效值,我们提出了特征值存在性和不存在性的验证方法。13数值计算表明,这种方法比现有的方法更简单有效,而且还开发了一个计算Bessel函数值的软件包,保证了计算的精度。它是在INTLAB区间计算库上构建的,并在MATLAB上进行了验证计算
项目成果
期刊论文数量(8)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Nakao, M.T., Watanabe, Y., Yamamoto, N.: "Verified numerical computations for an inverse elliptic eigenvalue problem with finite data"Japan Journal of Industrial and Applied Mathematics. Vo1.18. No.2. 163-173 (2001)
Nakao, M.T.、Watanabe, Y.、Yamamoto, N.:“用有限数据验证逆椭圆特征值问题的数值计算”日本工业与应用数学杂志。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Nakao, M.T., Watanabe, Y, Yamamoto, N: "Verified numerical computations for an inverse elliptic eigenvalue problem with finite data"Japan Journal of Industrial and Applied Mathematics. 18. 587-602 (2001)
Nakao, M.T.、Watanabe, Y、Yamamoto, N:“用有限数据验证逆椭圆特征值问题的数值计算”日本工业与应用数学杂志。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Nakao, M.T., Yamamoto, N.: "A guaranteed bound of the optimal constant in the error estimates for linear triangular element"(G.Alefelt, X.Chen (eds.)) Topics in Numerical Analysis With Special Emphasis on Nonlinear Problems, Computing Supplement 15, (Spri
Nakao, M.T.、Yamamoto, N.:“线性三角单元误差估计中最优常数的保证界限”(G.Alefelt、X.Chen(编辑))特别强调非线性问题的数值分析主题,
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Yamamoto, N: "A simple method for error bounds of eigenvalues of symmetric matrices"Linear Algebra and its Applications. 324. 227-234 (2001)
Yamamoto, N:“对称矩阵特征值误差界的简单方法”线性代数及其应用。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Nakao, M.T., Yamamoto, N.: "A guaranteed bound of the optimal constant in the error estimates for linear triangular element Part II : Details"(U.Kulisch, R.Lohner, A.Facius (eds.)) Perspectives on Enclosure Methods, (Springer Wien) (New York). 265-276 (20
Nakao, M.T.,Yamamoto, N.:“线性三角形单元误差估计中最优常数的保证界限第二部分:详细信息”(U.Kulisch、R.Lohner、A.Facius(编辑))外壳透视
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
YAMAMOTO Nobito其他文献
YAMAMOTO Nobito的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('YAMAMOTO Nobito', 18)}}的其他基金
Library for Validated Computation of Differential Equations
用于验证微分方程计算的库
- 批准号:
24540115 - 财政年份:2012
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Validate Computation Library on Time Evolution Equations
验证时间演化方程的计算库
- 批准号:
21540115 - 财政年份:2009
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Development of numerical verification methods on evolution equations
演化方程数值验证方法的发展
- 批准号:
19540118 - 财政年份:2007
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Numerical Verification Methods for Dynamical Systems described by ODEs
常微分方程描述的动力系统数值验证方法
- 批准号:
17540106 - 财政年份:2005
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Self-validated computation of singular integral and integral equations
奇异积分和积分方程的自验证计算
- 批准号:
15540111 - 财政年份:2003
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Development of practical methods for rigorous calculation with guaranteed accuracy
开发可保证精度的严格计算的实用方法
- 批准号:
09640278 - 财政年份:1997
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
相似海外基金
Structural calculation method of seismically isolated buildings against long-period ground motion: Reconstruction of response spectrum method
抗长周期地震动的隔震建筑结构计算方法:反应谱重建法
- 批准号:
17K06658 - 财政年份:2017
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Study of the dynamic stability derivative evaluation of the aircraft by the time and space spectrum method CFD
时空谱法CFD飞机动态稳定性导数评估研究
- 批准号:
15K14248 - 财政年份:2015
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
Development of Penetrant Testing Accurate Flow Rate Measurement System in Bent Pipe Flow by using Spread Spectrum Method
扩频法渗透探伤弯管流精确流量测量系统的研制
- 批准号:
25289353 - 财政年份:2013
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Ductility Inverse-Mapping Capacity Spectrum Method for Variable Level of Ground Motion
变水平地震动的延性反映射能力谱法
- 批准号:
23656340 - 财政年份:2011
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
Acoustoelastic Spectrum Method for Nondestructive Residual Stress Measurements
用于无损残余应力测量的声弹谱法
- 批准号:
03650091 - 财政年份:1991
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for General Scientific Research (C)
Novel Approach to Ultrasonic Transducer Characterization Using the Extended Angular Spectrum Method
使用扩展角谱方法表征超声波换能器的新方法
- 批准号:
8908084 - 财政年份:1989
- 资助金额:
$ 1.6万 - 项目类别:
Continuing Grant
Discrimination and Simultaneous Determination of Analogs by Derivative Spectrum Method
导数谱法鉴别及类似物的同时测定
- 批准号:
63571027 - 财政年份:1988
- 资助金额:
$ 1.6万 - 项目类别:
Grant-in-Aid for General Scientific Research (C)
Research Initiation: Extension of the Angular Spectrum Method to Characterize Ultrasonic Propagation in Tissue Like(Inhomogeneous) Media
研究启动:扩展角谱方法来表征组织类(非均匀)介质中的超声波传播
- 批准号:
8504602 - 财政年份:1985
- 资助金额:
$ 1.6万 - 项目类别:
Standard Grant
Thermal Histories of Crustal Rocks From the 40ar/39ar Age Spectrum Method
40ar/39ar年龄光谱法的地壳岩石热史
- 批准号:
8121275 - 财政年份:1982
- 资助金额:
$ 1.6万 - 项目类别:
Standard Grant
Error Evaluation of Inelastic Response Spectrum Method For Earthquake Design
地震设计非弹性反应谱法误差评估
- 批准号:
7822847 - 财政年份:1979
- 资助金额:
$ 1.6万 - 项目类别:
Standard Grant