检索结果-南通市图书馆

ON NON-ISOTROPIC JACOBI PSeUDOSPeCTRAL MeTHOD

在线全文

学校读者我要写书评

暂无评论

Journal of computational mathematics 2008年第4期26卷 511-535页

作者： benyu guo Keji 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 department of mathematics Shanghai Normal University Shanghai 200234

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.

关键词： Jacobi pseudospectral method in multiple dimensions Jacobi-Gauss type inter-polation Bernstein-Jackson type inequalities Singular problem Problem on axisymmetricdomain.

Some progress in spectral methods Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday

在线全文

学校读者我要写书评

暂无评论

science china mathematics 2013年第12期56卷 2411-2438页

作者： guo benyu department of mathematics Shanghai Normal University Scientific Computing Key Laboratory of shanghai universities division of computational science E-institute of Shanghai Universities

In this paper, we review some results on the spectral methods. We first consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems, including degenerated and singular differential equations. Then we present the generalized Jacobi quasi-orthogonal approximation and its applica- tions to the spectral element methods for high order problems with mixed inhomogeneous boundary conditions. We also discuss the related spectral methods for non-rectangular domains and the irrational spectral methods for unbounded domains. Next, we consider the Hermite spectral method and the generalized Hermite spec- tral method with their applications. Finally, we consider the Laguerre spectral method and the generalized Laguerre spectral method for many problems defined on unbounded domains. We also present the generalized Laguerre quasi-orthogonal approximation and its applications to certain problems of non-standard type and exterior problems.

关键词： Jacobi Hermite and Laguerre spectral approximations Jacobi and Laguerre quasi-orthogonalapproximations spectral and spectral element methods degenerated and singular problems problems on non-rectangular and unbounded domains problems of non-standard type exterior problems

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

在线全文

学校读者我要写书评

暂无评论

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

Legendre rational approximation on the whole line

在线全文

学校读者我要写书评

暂无评论

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

在线全文

学校读者我要写书评

暂无评论

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.

A NeW PSeUDOSPeCTRAL MeTHOD ON QUADRILATeRALS

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

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.

SPeCTRAL MeTHOD FOR MIXeD INHOMOGeNeOUS BOUNDARY VALUe PROBLeMS IN THRee DIMeNSIONS

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

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.

Legendre Rational Spectral Method for Nonlinear Klein-Gordon equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Numerical mathematics A Journal of Chinese universities(english Series) 2006年第2期15卷 143-149页

作者： Zhongqing Wang benyu guo department of mathematics Division of Computational Science of E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China

A Legendre rational spectral method is proposed for the nonlinear Klein-Gordon equation on the whole line. Its stability and convergence are proved. Numerical results coincides well with the theoretical analysis and d... 详细信息

关键词：勒让德有理数光谱方法非线性方程克莱因-戈登方程收敛稳定性

ReMARKS ON eRROR eSTIMATeS FOR THe TRUNC PLATe eLeMeNT

在线全文

学校读者我要写书评

暂无评论

Journal of computational mathematics 2006年第1期24卷 103-112页

作者： Ling guo Jian-guo Huang Zhong-ci Shi department of mathematics Shanghai Jiao Tong University Shanghai 200030 China China LSeC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

This paper provides a simplified derivation for error estimates of the TRUNC plate element. The error analysis for the problem with mixed boundary conditions is also discussed.

关键词： Plate bending problems TRUNC element error estimates