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Laguerre Spectral Method for High Order Problems

Published online by Cambridge University Press:  28 May 2015

Chao Zhang ,
Ben-Yu Guo  and
Tao Sun
Chao Zhang*
Affiliation:
Department of Mathematics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, China
Ben-Yu Guo*
Affiliation:
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China; & Scientific Computing Key Laboratory of Shanghai Universities; &Division of Computational Science of E-institute of Shanghai Universities
Tao Sun*
Affiliation:
Department of Applied Mathematics, Shanghai Finance University, Shanghai, 201209, China
*
Corresponding author.Email address:zcxzl977@163.com
Corresponding author.Email address:byguo@shnu.edu.en
Corresponding author.Email address:taosun80@yeah.net
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Abstract

In this paper, we propose the Laguerre spectral method for high order problems with mixed inhomogeneous boundary conditions. It is also available for approximated solutions growing fast at infinity. The spectral accuracy is proved. Numerical results demonstrate its high effectiveness.

Keywords

65L6065M70Laguerre spectral methodhigh order problems with mixed inhomogeneous boundary conditions
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 3 , August 2013 , pp. 520 - 537
Copyright
Copyright © Global Science Press Limited 2013

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References

[1] Auteri, F., Parolini, N. and Quartapelle, L., Essential imposition of Neumann condition in Galerkin-Legendre elliptic solver, J. Comput. Phys., 185(2003), pp. 427–444.Google Scholar
[2] Bernardi, C. and Maday, Y., Spectral methods, in Handbook of Numerical Analysis, Vol.5, Techniques of Scientific Computing, pp. 209–486, ed. by Ciarlet, P G. and Lions, J.L., Elsevier, Amsterdam, 1997.Google Scholar
[3] Boyd, J.P., Chebyshev and Fourier Spectral Methods, the second edition, Dover Publication Inc., Mineda, New York, 2001.Google Scholar
[4] Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 2006.Google Scholar
[5] Coullet, P., Elphick, C. and Repaux, D., Nuture of spatial chaos, Phys. Rev. Lett., 58 (1987), pp. 431–434.Google Scholar
[6] Everitt, W. N., Littlejohn, L. L. and Wellman, R., The Sobolev orthogonality and spectral analysis of the Laguerre polynomials for positive integers k* , J. Comput. Appl. Math., 171 (2004), pp. 199–234.Google Scholar
[7] Funaro, D., Polynomial Approximations of Differential Equations, Springer-Verlag, Berlin, 1992.Google Scholar
[8] Gottlieb, D. and Orszag, S. A., Numerical Analysis of Spectral Methods: Theory and Applications, SIAM-CBMS, Philadelphia, 1977.Google Scholar
[9] Guo, Ben-Yu, Spectral Methods and Their Applications, World Scientific, Singapore, 1998.Google Scholar
[10] Guo, Ben-Yu and Jiao, Yu-Jian, Mixed generalized Laguerre-Fourier spectral method for exterior problem of Navier-Stokes equations, Disc. Cont. Dyna. Syst. B, 11 (2009), pp. 315–345.Google Scholar
[11] Guo, Ben-Yu and Shen, Jie, Laguerre-Galerkin methodfor nonlinear partial differential equations on a semi-infinite interval, Numer. Math., 86 (2000), pp. 635–654.Google Scholar
[12] Guo, Ben-Yu, Shen, Jie and Xu, Cheng-Long, Generalized Laguerre approximation and its applications to exterior problems, J. Comput. Math., 23 (2005), pp. 113–130.Google Scholar
[13] Guo, Ben-Yu, Sun, Tao and Zhang, Chao, Jacobi and Laguerre quasi-orthogonal approximations and related interpolation, Math. Comput., 82 (2013), pp. 413–441.Google Scholar
[14] Guo, Ben-Yu and Wang, Tian-Jun, Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an infinite channel, Math. Comput., 78 (2009), pp. 129–151.Google Scholar
[15] Guo, Ben-Yu and Xu, Cheng-Long, Mixed Laguerre-Legendre pseudospectral method for incompressible fluid flow in an infinite strip, Math. Comput., 72 (2003), pp. 95–125.Google Scholar
[16] Guo, Ben-Yu, Zhang, Chao and Sun, Tao, Some developments in spectral methods, Studies in Adv. Math., 51 (2011), pp. 561–574.Google Scholar
[17] Guo, Ben-Yu and Zhang, Xiao-Yong, A new generalized Laguerre spectral approximation and its applications, J. Comput. Appl. Math., 181 (2005), pp. 342–363.Google Scholar
[18] Karniadakis, G. E. and Sherwin, S. J., Spectral/hp Element Methods for CFD, The Second Edition, Oxford Univ. Press, Oxford, 2005.Google Scholar
[19] Shen, Jie, Stable and efficient spectral methods in unbounded domains using Laguerre functions, SIAM J. Numer. Anal., 38 (2000), pp. 1113–1133.Google Scholar
[20] Xu, Cheng-Long and Guo, Ben-Yu, Laguerre pseudospectral method for nonlinear partial differential equation, J. Comput. Math., 20 (2002), pp. 413–428.Google Scholar