XU Cheng-long, GUO Ben-yu. Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions[J]. Applied Mathematics and Mechanics, 2008, 29(3): 281-300.
Citation: XU Cheng-long, GUO Ben-yu. Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions[J]. Applied Mathematics and Mechanics, 2008, 29(3): 281-300.

Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions

  • Received Date: 2007-12-12
  • Rev Recd Date: 2008-01-24
  • Publish Date: 2008-03-15
  • The Laguerre spectral and pseudospectral methods for multiple-dimensional nonlinear partial differential equations are investigated. Some results on the modified Laguerre orthogonal approximation and interpolation were established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods were proposed for two-dimensional Logistic equation. The stability and convergence of suggested schemes were proved. Numerical results demonstrate the high accuracy of these approaches.
  • loading
  • [1]
    Maday Y,Bernaud-Thomas B,Vandeven H.Une re[KG-*4]. h′abilitation des méthods spectrales de type Laguerre[J].Rech Aérospat,1985,6(6):353-379.
    [2]
    Funaro D.Polynomial Approximation of Differential Equations[M].Berlin: Springer-Verlag,1992.
    [3]
    GUO Ben-yu,SHEN Jie.Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval[J].Numer Math,2000,86(4):635-654. doi: 10.1007/PL00005413
    [4]
    GUO Ben-yu,WANG Li-lian,WANG Zhong-qing.Generalized Laguerre interpolation and pseudospectral method for unbounded domains[J].SIAM J Numer Anal,2006,43(6):2567-2589. doi: 10.1137/04061324X
    [5]
    GUO Ben-yu,ZHANG Xiao-yong.A new generalized Laguerre approximation and its applications[J].J Comput Appl Math,2005,181(2):342-363. doi: 10.1016/j.cam.2004.12.008
    [6]
    GUO Ben-yu,XU Cheng-long.Mixed Laguerre-Lagendre pseudospectral method for incompressible fluid flow in an infinite strip[J].Math Comp,2003,73(245):95-125. doi: 10.1090/S0025-5718-03-01521-7
    [7]
    Mastroianni G,Monegato G.Nystrm interpolants based on zeros of Laguerre polynomials for some weiner-Hopf equations[J].IMA J Numer Anal,1997,17(4):621-642. doi: 10.1093/imanum/17.4.621
    [8]
    SHEN Jie.Stable and efficient spectral methods in unbounded domains using Laguerre functions[J].SIAM J Numer Anal,2000,38(4):1113-1133. doi: 10.1137/S0036142999362936
    [9]
    XU Cheng-long,GUO Ben-yu.Laguerre pseudospectral method for nonlinear partial differential equations in unbounded domains[J].J Comput Math,2002,20(4):413-428.
    [10]
    Bergh J,Lfstrm J.Interpolation Spaces, An Introduction[M].Berlin: Spring-Verlag,1976.
    [11]
    Bernardi C,Maday Y.Spectral Methods[A].In:Ciarlet P G,Lions J L,Eds.Handbook of Numerical Analysis[C].Amsterdam: Elsevier,1997,209-486.
    [12]
    GUO Ben-yu.Generalized stability of discretization and its applications to numerical solutions of nonlinear differential equations[J].Contemp Math,1994,163:33-54. doi: 10.1090/conm/163/01548
    [13]
    GUO Ben-yu.Error estimation of Hermite spectral method for nonlinear partial differential equations[J].Math Comp,1999,68(227):1067-1078. doi: 10.1090/S0025-5718-99-01059-5
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2871) PDF downloads(654) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return