Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions
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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.
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关键词:
- 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. -
[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.Nystrm 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,Lfstrm 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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