105
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Spectral method for multi-dimensional problems of high order on unbounded domains using generalized Laguerre functions

, &
Pages 2040-2059 | Received 01 Aug 2019, Accepted 03 Jul 2020, Published online: 17 Feb 2021

References

  • M.M. Alsuyuti, E.H. Doha, S.S. Ezz-Eldien, B.I. Bayoumi, and D. Baleanu, Modified Galerkin algorithm for solving multitype fractional differential equations, Math. Methods Appl. Sci. 42 (2019), pp. 1389–1412.
  • C. Bernardi and Y. Maday, Spectral methods, in Handbook of Numerical Analysis. Techniques of Scientific Computing 5, P.G. Ciarlet and J.L. Lions, eds., Elsevier, Amsterdam, 1997, pp. 209–486.
  • J. P. Boyd, The optimization of convergence for Chebyshev polynomial methods in an unbounded domain, J. Comput. Phys. 45(1) (1982), pp. 43–79.
  • J.P. Boyd, Chebyshev and Fourier Spectral Methods, Springer, New York, 2001.
  • C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer, Berlin, 2006.
  • O. Coulaud, D. Funaro, and O. Kavian, Laguerre spectral approximation of elliptic problems in exterior domains, Comput. Methods Appl. Mech. Eng. 80 (1990), pp. 451–458.
  • S.S. Ezz-Eldien, On solving systems of multi-pantograph equations via spectral tau method, Appl. Math. Comput. 321 (2018), pp. 63–73.
  • S.S. Ezz-Eldien and E.H. Doha, Fast and precise spectral method for solving pantograph type Volterra integro-differential equations, Numer. Algor. 81 (2019), pp. 57–77.
  • D. Funaro and O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite function, Math. Comp. 57 (1991), pp. 597–619.
  • D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, Society for Industrial and Applied Mathematics, Philadelphia, 1987.
  • B.Y. Guo, J. Shen, and L.L. Wang, Optimal spectral-Galerkin methods using generalized Jacobi polynomials, J. Sci. Comput. 27(1–3) (2006), pp. 305–322.
  • B.Y. Guo, J. Shen, and L.L. Wang, Generalized Jacobi polynomials/functions and their applications, Appl. Numer. Math. 59 (2009), pp. 1011–1028.
  • B.Y. Guo, T. Sun, and C. Zhang, Jacobi and Laguerre quasi-orthogonal approximations and related interpolations, Math. Comp. 82 (2013), pp. 413–441.
  • F.J. Liu, H.Y. Li, and Z.Q. Wang, Spectral methods using generalized Laguerre functions for second and fourth order problems, Numer. Algorithms 75 (2017), pp. 1005–1040.
  • F.J. Liu, Z.Q. Wang, and H.Y. Li, A fully diagonalized spectral method using generalized Laguerre functions on the half line, Adv. Comput. Math. 43 (2017), pp. 1227–1259.
  • H.P. Ma, W.W. Sun, and T. Tang, Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains, SIAM J. Numer. Anal. 43 (2005), pp. 58–75.
  • J. Shen, Efficient spectral-Galerkin method I. direct solvers for second- and fourth-order equations by using Legendre polynomials, SIAM J. Sci. Comput. 15(6) (1994), pp. 1489-–1505.
  • J. Shen, Stable and efficient spectral methods in unbounded domains using Laguerre functions, SIAM J. Numer. Anal. 38 (2000), pp. 1113–1133.
  • J. Shen and L.L. Wang, Some recent advances in spectral methods for unbounded domains, Commun. Comput. Phys. 5 (2009), pp. 195–141.
  • J. Shen, T. Tang, and L.L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Vol. 41, Series in Computational Mathematics, Springer, Berlin, 2011.
  • T. Sun and B.Y. Guo, Generalized Jacobi approximation in multiple dimensions and applications, J. Sci. Comput. 6 (2013), pp. 327–350.
  • C. Zhang and B.Y. Guo, Domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equation on unbounded domains, J. Sci. Comput. 53 (2012), pp. 451–480.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.