Mixed Fourier-Laguerre Spectral and Pseudospectral Methods for Exterior Problems Using Generalized Laguerre Functions

In this paper, we develop the mixed spectral and pseudospectral methods for two-dimensional exterior problems, by using the scaled generalized Laguerre functions. Some basic results on the mixed Fourier-Laguerre orthogonal approximation and Gauss-type interpolation are established, which play important roles in the related spectral and pseudospectral methods. As an example, we propose the mixed spectral and pseudospectral schemes for a model problem. The convergence of proposed schemes are proved. Numerical results demonstrate the spectral accuracy efficiency of this new approach.

[1]  Jie Shen,et al.  Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions , 2000, SIAM J. Numer. Anal..

[2]  Jie Shen,et al.  Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval , 2000, Numerische Mathematik.

[3]  Giovanni Monegato,et al.  Nyström interpolants based on zeros of Laguerre polynomials for some Weiner-Hopf equations , 1997 .

[4]  B. Guo,et al.  Spectral method for differential equations of degenerate type on unbounded domains by using generalized Laguerre functions , 2007 .

[5]  Jie Shen,et al.  Irrational approximations and their applications to partial differential equations in exterior domains, , 2008, Adv. Comput. Math..

[6]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[7]  G. Ben-yu,et al.  Spherical Harmonic–Generalized Laguerre Spectral Method for Exterior Problems , 2006, J. Sci. Comput..

[8]  Zhongqing Wang,et al.  Mixed spectral method for three-dimensional exterior problems using spherical harmonic and generalized Laguerre functions , 2008 .

[9]  G. Ben-yu,et al.  Generalized Laguerre Interpolation and Pseudospectral Method for Unbounded Domains , 2006 .

[10]  Y. Maday,et al.  Une réhabilitation des méthodes spectrales de type Laguerre , 1985 .

[11]  B. Guo,et al.  A new generalized Laguerre spectral approximation and its applications , 2005 .

[12]  G. Mastroianni,et al.  Lagrange Interpolation at Laguerre Zeros in Some Weighted Uniform Spaces , 2001 .

[13]  Zhong-Qing Wang,et al.  PSEUDOSPECTRAL METHOD USING GENERALIZED LAGUERRE FUNCTIONS FOR SINGULAR PROBLEMS ON UNBOUNDED DOMAINS , 2009 .

[14]  B. Guo,et al.  Hermite pseudospectral method for nonlinear partial differential equations , 2000 .

[15]  B. Guo,et al.  GENERALIZED LAGUERRE APPROXIMATION AND ITS APPLICATIONS TO EXTERIOR PROBLEMS , 2005 .

[16]  D. Funaro Polynomial Approximation of Differential Equations , 1992 .

[17]  B. Guo,et al.  Spectral Methods and Their Applications , 1998 .

[18]  B. Guo,et al.  Modified Laguerre spectral and pseudospectral methods for nonlinear partial differential equations in multiple dimensions , 2008 .