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

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^1,2,
郭本瑜^2,3,4

1.
同济大学数学系,上海 200092;2.上海高校计算科学E_研究院,上海 200234;3.上海师范大学数学系,上海 200234;4.上海高校科学计算重点实验室,上海 200234

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
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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

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

XU Cheng-long^1,2,
GUO Ben-yu^2,3,4

1.
Department of Mathematics, Tongji University, Shanghai 200092, P. R. China;

摘要

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．
- 多维区域 /
- 修正Laguerre正交多项式 /
- 插值与正交逼近 /
- 谱与拟谱方法
Abstract: 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.
- multiple dimension /
- modified Laguerre orthogonal polynomials /
- interporlation and orthogonal approximation /
- spectral and pseudospectral method

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参考文献(13)

[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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多维区域中非线性偏微分方程的修正Laguerre谱与拟谱方法

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).

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

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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

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).

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出版历程

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

计量

出版历程

目录

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).