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ON NON-ISOTROPIC JACOBI PSEUDOSPECTRAL METHOD

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.

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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.

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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

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