Synthetic approach for the development of computer assisted analysis from the numerical verification methods
从数值验证方法发展计算机辅助分析的综合方法
基本信息
- 批准号:15204007
- 负责人:
- 金额:$ 20.63万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (A)
- 财政年份:2003
- 资助国家:日本
- 起止时间:2003 至 2006
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In this research, we newly developed the numerical verification methods which can be applied to wide mathematical and analytical problems, as well as extended or improved the existing techniques.And we actually applied these methods to particular problems such as equations in the mathematical fluid mechanics and oscillation problems etc. The important research results obtained by investigators and co-investigators are as follows :1.Nakao, N.Yamamoto, Watanabe established several refinements and extensions for the constructive error estimates for the finite finite element projections of the Poisson and the bi-harmonic equations on various kinds of domains, particularly, on nonconvex polygonal domains. These results played important and essential roles for the numerical verification of solutions of nonlinear elliptic equations and the two dimensional stationary Navier-Stokes problems.2.Nagatou numerically proved the stability of the flow on the torus called Kolmogorov problem.3.Minamoto presented a formulation of the verification condition for the double turning point and applied it to the perturbed Gelfand equation.4.Oishi established some refinements on the fast algorithm for the solutions of linear equations.5.Nishida et al. presented the computed results with guaranteed error bounds for the symmetry breaking bifurcation point of the solution of two dimensional heat convection problems, as well as they formulated the numerical verification algorithm for the three dimensional problems with some prototypical verified examples.6.Chin obtained some numerical verification results on the existence of solutions and a posteriori error estimates for the linear complementarity problems.
在这项研究中,我们开发了新的数值验证方法,可以应用于广泛的数学和分析问题,并扩展或改进了现有的技术。我们实际上把这些方法应用到一些特殊的问题上,比如数学流体力学方程和振动问题等等。研究者及合作研究者取得的重要研究成果如下:1.研究成果;Nakao, N.Yamamoto, Watanabe对泊松方程和双调和方程在各种域上,特别是在非凸多边形域上的有限有限元投影的建设性误差估计建立了若干改进和扩展。这些结果对于非线性椭圆方程解的数值验证和二维平稳Navier-Stokes问题的数值验证具有重要的意义。Nagatou用数值方法证明了环面上流动的稳定性,称为Kolmogorov问题。Minamoto给出了双拐点验证条件的公式,并将其应用于摄动Gelfand方程。Oishi对求解线性方程的快速算法进行了改进。Nishida等人给出了二维热对流问题解的对称破缺分岔点有保证误差界的计算结果,并通过一些原型验证实例,制定了三维问题的数值验证算法。得到了线性互补问题解存在性的数值验证结果和后验误差估计。
项目成果
期刊论文数量(104)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Numerical Verification of Solutions of Nekrasov's Integral Equation
Nekrasov积分方程解的数值验证
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:Murashige;S.
- 通讯作者:S.
Some computer assistedproofs for solutions of the heat convectionproblems
解决热对流问题的一些计算机辅助证明
- DOI:
- 发表时间:2003
- 期刊:
- 影响因子:0
- 作者:M.T.Nakao;Y.Watanabe;N.Yamamoto;T.Nishida
- 通讯作者:T.Nishida
Ryoo, C-S.: "Numerical verification of solutions for obstacle problems"Journal of computational and Applied Mathematics. 161. 405-416 (2003)
Ryoo, C-S.:“障碍问题解决方案的数值验证”计算与应用数学杂志。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Nakao, M.T.: "An efficient approach to the numerical verification for solutions of elliptic differential equations"Numerical Algorithms, Special issue for Proceedings of SCAN2002. (掲載決定).
Nakao, M.T.:“椭圆微分方程解的数值验证的有效方法”,数值算法,SCAN2002 论文集特刊(已出版)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
A computational approach to constructive a priori and a posteriori error estimates for finite element approximations of bi-harmonic problems
双调和问题有限元近似的构造性先验和后验误差估计的计算方法
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:Nakao;M.T.
- 通讯作者:M.T.
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NAKAO Mitsuhiro其他文献
NAKAO Mitsuhiro的其他文献
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{{ truncateString('NAKAO Mitsuhiro', 18)}}的其他基金
A study on the numerical verification method of solutions with high accuracy for the nonlinear mathematical models in infinite dimension
无限维非线性数学模型高精度解的数值验证方法研究
- 批准号:
15K05012 - 财政年份:2015
- 资助金额:
$ 20.63万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Numerical verification method of solutions for nonlinear evolutional equations
非线性演化方程解的数值验证方法
- 批准号:
24540151 - 财政年份:2012
- 资助金额:
$ 20.63万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Development of computer assisted analysis for complicated nonlinear phenomena
复杂非线性现象计算机辅助分析的发展
- 批准号:
20224001 - 财政年份:2008
- 资助金额:
$ 20.63万 - 项目类别:
Grant-in-Aid for Scientific Research (S)
Asymptotic behaivours of solutions for nonlinear wave equations
非线性波动方程解的渐近行为
- 批准号:
17340040 - 财政年份:2005
- 资助金额:
$ 20.63万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Synthetic approach for new developments of self-validating numerics
自验证数值新发展的综合方法
- 批准号:
13440035 - 财政年份:2001
- 资助金额:
$ 20.63万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Exterior problem for nonlinear wave equations
非线性波动方程的外问题
- 批准号:
13440049 - 财政年份:2001
- 资助金额:
$ 20.63万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Stabilization problem for nonlinear wave eq
非线性波方程的镇定问题
- 批准号:
10440053 - 财政年份:1998
- 资助金额:
$ 20.63万 - 项目类别:
Grant-in-Aid for Scientific Research (B).
相似海外基金
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:
$ 20.63万 - 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:
$ 20.63万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Validated computation of patterns in recurrent neural networks
循环神经网络中模式的验证计算
- 批准号:
493789610 - 财政年份:
- 资助金额:
$ 20.63万 - 项目类别:
WBP Position