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Legendre rational approximation on the whole line

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Science China Mathematics 2004年第Z1期47卷 155-164页

作者： guo benyu WANG Zhongqing Department of Mathematics Shanghai Normal University Division of Scientific ComputationE-Institute of Shanghai Universities Shanghai 200234 China Department of Mathematics Shanghai Normal University Division of Scientific ComputationE-Institute of Shanghai Universities Shanghai 200234 China

The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numeri... 详细信息

关键词： Legendre rational approximation spectral method on the vrhole line.

SPECTRAL AND SPECTRAL ELEMENT METHODS FOR HIGH ORDER PROBLEMS WITH MIXED BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2014年第4期32卷 392-411页

作者： benyu guo Chao Zhang Department of Mathematics Shanghai Normal University Shanghai 200234 China Scientific Computing Key Laboratory of Shanghai Universities Division of Computational Science of E-institute of Shanghai Universities Shanghai 200234 China Department of Mathematics Jiangsu Normal University Xuzhou 221116 China

In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.

关键词： Spectral and spectral element methods~ High order problems with mixedinhomogeneous boundary conditions.

Petrov-Galerkin Spectral Element Method for Mixed Inhomogeneous Boundary Value Problems on Polygons

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Chinese Annals of Mathematics,Series B 2010年第6期31卷 855-878页

作者： Hongli JIA benyu guo Department of Mathematics Shanghai Normal University Shanghai 200234 China Department of Mathematics Donghua University Shanghai 200065 China. Department of Mathematics Shanghai Normal University Scientific Computing Key Laboratory of Shanghai Universities Shanghai E-institute for Computational Science Shanghai 200234 China

The authors investigate Petrov-Galerkin spectral element method. Some results on Legendre irrational quasi-orthogonal approximations are established, which play important roles in Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems of partial differential equations defined on polygons. As examples of applications, spectral element methods for two model problems, with the spectral accuracy in certain Jacobi weighted Sobolev spaces, are proposed. The techniques developed in this paper are also applicable to other higher order methods.

关键词： Legendre quasi-orthogonal approximation Petrov-Galerkin spectral element method Mixed inhomogeneous boundary value problems

A NEW PSEUDOSPECTRAL METHOD ON QUADRILATERALS

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Journal of Computational Mathematics 2016年第4期34卷 365-384页

作者： benyu guo Hongli Jia Shanghai Normal University 200234 Shanghai P.R. China Scientific Computing Key Laboratory of Shanghai Universities Division of Computational Science of E-institute of Shanghai Universities Department of Mathematics Donghua University 200065 Shanghai P.R. China

In this paper, we investigate a new pseudospectral method for mixed boundary value problems defined on quadrilaterals. We introduce a new Legendre-Gauss type interpolation and establish the basic approximation results, which play important roles in pseudospectral method for partial differential equations defined on quadrilaterals. We propose pseudospee- tral method for two model problems and prove their spectral accuracy. Numerical results demonstrate their high efficiency. The approximation results developed in this paper are also applicable to other problems defined on complex domains.

关键词： Legendre-Gauss type interpolation on quadrilaterals Pseudospectral methodof mixed boundary value problems.

Zing-Yang Kuo and behavior epigenesis based on animal experiments

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Protein & Cell 2020年第6期11卷 387-390页

作者： Yanyan Qian Wei Chen benyu guo School of psychology Nanjing Normal UniversityNanjing 210097China Department of psychology Shaoxing UniversityShaoxing 312000China Department of psychology The Education University of Hong KongHongkongChina

Zing-Yang Kuo(1898-1970)(Fig.1),styled Taofu,was a world-renowned Chinese *** was one of the most extreme precursors of the behaviorism school and the most radical behaviorist in the history of behavioristic *** main ... 详细信息

关键词： behavior extreme renowned

SPECTRAL METHOD FOR MIXED INHOMOGENEOUS BOUNDARY VALUE PROBLEMS IN THREE DIMENSIONS

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Journal of Computational Mathematics 2012年第6期30卷 579-600页

作者： Tianjun Wang benyu guo Wei Li Department of Mathematics Henan University of Science and Technology Luo Yang 471003 China Department of Mathematics Shanghai Normal University Shanghai 200235 China Scientific Computing Key Laboratory of Shanghai UniversitiesDivision of Computational Science of E-Institute of Shanghai Universities

In this paper, we investigate spectral method for mixed inhomogeneous boundary value problems in three dimensions. Some results on the three-dimensional Legendre approxima- tion in Jacobi weighted Sobolev space are established, which improve and generalize the existing results, and play an important role in numerical solutions of partial differential equations. We also develop a lifting technique, with which we could handle mixed inho- mogeneous boundary conditions easily. As examples of applications, spectral schemes are provided for three model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms is proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy, and confirm the theoretical analysis well.

关键词： Three-dimensional Legendre approximation in Jacobi weighted Sobolev space,Lifting technique Spectral method for mixed inhomogeneous boundary value problems.

Tsai Chiao:The founder of physiology and aviation,aerospace and navigation medicine in China

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Protein & Cell 2022年第11期13卷 779-784页

作者： Yalan Wang Zijian Li Yanyan Qian benyu guo Psychology College Nanjing Normal UniversityNanjing 210097China Social and Behavioural Sciences Faculty Leiden University2333 AK LeidenNetherlands

On February 16th,2019,Tsai Academician Museum held a launch ceremony of a minor planet(207681)'s settling in Jieyang County,Guangdong *** minor planet was given a new name Cai Qiao(Fig.1)on October 14th,*** Qiao was discovered at Xu Yi Station in the Purple Hills Observatory of the Chinese Academy of Sciences on August 16th,*** who is the planet named after?

关键词： Academician planet aviation

Generalized Jacobi-Gauss-Lobatto interpolation

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Frontiers of Mathematics in China 2013年第4期8卷 933-960页

作者： Zhengsu WAN benyu guo Chengjian ZHANG School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074 China Department of Mathematics Hunan Institute of Science and Technology Yueyang 414006China Department of Mathematics Shanghai Normal University Shanghai 200234 China

We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order problems. We establish some results on these interpolations in non-uniformly weighted Sobolev spaces, which serve as the basic tools in analysis of numerical quadratures and various numerical methods of differential and integral equations.

关键词： Generalized Jacobi-Gauss-Lobatto interpolation pseudospectral method non-uniformly weighted Sobolev space

CHEBYSHEV　SPECTRAL-FINITE　ELEMENT　METHOD　FOR　INCOMPRESSIBLE　FLUID　FLOW

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Applied Mathematics(A Journal of Chinese Universities) 1996年第4期11卷 377-398页

作者： guo benyu and He Songnian Department of Mathematics Shanghai University of Science and Technology Shanghai China

In this paper, we propose a mixed method for solving two-dimensional unsteady vorticity equations by using Chebyshev spectral-finite element *** generalized stability and the optimal rate of convergence are proved. The numericalresults show the advantages of such method. The technique in this paper is also useful for other nonlinear problems.

关键词： Chebyshev spectral-finite element approximation two-dimensional vorticity equation.