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| A GENERALIZED GAUSS-TYPE QUADRATURE FORMULA AND ITS APPLICATIONS TO PSEUDOSPECTRAL METHOD | |
| 作者姓名： | 王立联 郭本瑜 王中庆 |
| 作者单位： | Department of Mathematics，Department of Mathematics，Laboratory of Computational Physics Shanghai Normal University，Shanghai 200234，PRC，Shanghia Normal University，Shanghai 200234，PRC，Institute of Applied Physics and Computational Mathematics，Beijing 100088，PRC |
| 基金项目： | TheworkofthefirstauthorispartiallysupportedbyShanghaiNaturalScienceFoundationN .0 0JC1 4 0 5 7,and ShanghiNaturalScienceFoundationforYouthN .0 1QN85 . TheworkofthesecondauthorispartiallysupportedbytheSpecialFundsforMajorStateBasicResearchProjectsofChin |
| 摘 要： | 1 ＩｎｔｒｏｄｕｃｔｉｏｎＳｐｅｃｔｒａｌｍｅｔｈｏｄｅｍｐｌｏｙｓｇｌｏｂａｌｐｏｌｙｎｏｍｉａｌｓａｓｔｒｉａｌｆｕｎｃｔｉｏｎｓｉｎｓｐａｔｉａｌｄｉｓｃｒｅｔｉｚａｔｉｏｎｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｉｔｏｆｔｅｎｐｒｏｖｉｄｅｓａｃｃｕｒａｔｅｎｕｍｅｒｉｃａｌｒｅｓｕｌｔｓｗｉｔｈｒｅｌａｔｉｖｅｌｙｌｅｓｓｄｅｇｒｅｅｏｆｆｒｅｅｄｏｍｓ,ａｎｄｔｈｕｓｈａｓｂｅｅｎｓｕｃｃｅｓｓｆｕｌｌｙｕｓｅｄｆｏｒｃｏｍｐｕｔａｔｉｏｎｓｉｎｓｃｉｅｎｃｅａｎｄｅｎｇｉｎ… |
A GENERALIZED GAUSS-TYPE QUADRATURE FORMULA AND ITS APPLICATIONS TO PSEUDOSPECTRAL METHOD |
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| Wang Lilian Guo Benyu,Wang Zhongqing.A GENERALIZED GAUSS-TYPE QUADRATURE FORMULA AND ITS APPLICATIONS TO PSEUDOSPECTRAL METHOD[J].Numerical Mathematics A Journal of Chinese Universities English Series,2002,11(2):179-196. | |
| Authors: | Wang Lilian Guo Benyu Wang Zhongqing |
| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, PRC 2. Department of Mathematics, Shanghia Normal University, Shanghai 200234, PRC 3. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, PRC |
| Abstract: | A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach. |
| Keywords: | generalized Gauss-type quadrature formula pseudospectral method K-S equa-tion |
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