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多维区域中非线性偏微分方程的修正Laguerre谱与拟谱方法

徐承龙 郭本瑜

徐承龙, 郭本瑜. 多维区域中非线性偏微分方程的修正Laguerre谱与拟谱方法[J]. 应用数学和力学, 2008, 29(3): 281-300.
引用本文: 徐承龙, 郭本瑜. 多维区域中非线性偏微分方程的修正Laguerre谱与拟谱方法[J]. 应用数学和力学, 2008, 29(3): 281-300.
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.

多维区域中非线性偏微分方程的修正Laguerre谱与拟谱方法

基金项目: 上海高校计算科学E-研究院基金资助(NE03004);上海市(重大)科技攻关资助项目(N075105118);上海市重点学科计划资助项目(NT0401)
详细信息
    作者简介:

    徐承龙(1963- ),男,上海人,教授,博士(联系人.Tel:+86-21-65983240;Fax:+86-22-65982341;E-mail:clxu601@online.sh.cn).

  • 中图分类号: O241.5;O241.82;O241.3

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

  • 摘要: 研究多维区域中非线性偏微分方程的谱与拟谱方法.建立了修正Laguerre正交逼近与插值结果,这些结果对于建立和分析无界区域中的数值方法起着重要的作用.作为结果的一个应用,研究了二维无界区域中的Logistic方程的修正Laguerre谱格式,证明了它的稳定性和收敛性.数值试验结果表明所提出方法具有很高的精度,与理论分析结果完全吻合.
  • [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
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出版历程
  • 收稿日期:  2007-12-12
  • 修回日期:  2008-01-24
  • 刊出日期:  2008-03-15

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