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Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (3): 311-331 .doi: https://doi.org/10.1007/s10483-008-0304-x

• Articles • 上一篇    下一篇

Modified Laguerre spectral and pseudospectral methods for nonlinear partial differential equations in multiple dimensions

徐承龙, 郭本瑜   

  • 收稿日期:2007-12-12 修回日期:2008-01-15 出版日期:2008-03-10 发布日期:2008-03-10
  • 通讯作者: 徐承龙

Modified Laguerre spectral and pseudospectral methods for nonlinear partial differential equations in multiple dimensions

XU Cheng-long, GUO Ben-yu   

    1. Department of Mathematics, Tongji University, Shanghai 200092, P. R. China;
    2. Division of Computational Science of E-institute of Shanghai Universities, Shanghai 200234, P. R. China;
    3. Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China;
    4. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, P. R. China
  • Received:2007-12-12 Revised:2008-01-15 Online:2008-03-10 Published:2008-03-10
  • Contact: XU Cheng-long

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Abstract: The Laguerre spectral and pseudospectral methods are investigated for multi-dimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.

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