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.