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Generalized Jacobi rational spectral methods with essential imposition of Neumann boundary conditions in unbounded domains
1. | Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China |
References:
[1] |
F. Auteri, N. Parolini and L. Quartapelle, Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers, J. Comput. Phys., 185 (2003), 427-444.
doi: 10.1016/S0021-9991(02)00064-5. |
[2] |
J. Bergh and J. Löfström, "Interpolation Spaces. An Introduction," Grundlehren der Mathematischen Wissenschaften, No. 223, Spring-Verlag, Berlin-New York, 1976. |
[3] |
C. Bernardi and Y. Maday, Spectral Methods, in "Handbook of Numerical Analysis, Vol. V," 209-485, North-Holland, Amsterdam, 1997. |
[4] |
J. P. Boyd, Spectral method using rational basis functions on an infinite interval, J. Comp. Phys., 69 (1987), 112-142.
doi: 10.1016/0021-9991(87)90158-6. |
[5] |
J. P. Boyd, Orthogonal rational functions on a semi-infinite interval, J. Comp. Phys., 70 (1987), 63-88.
doi: 10.1016/0021-9991(87)90002-7. |
[6] |
C. I. Christov, A complete orthonormal system of functions in $L^2(-\infty,\infty)$ space, SIAM J. Appl. Math., 42 (1982), 1337-1344.
doi: 10.1137/0142093. |
[7] |
Ben-yu Guo, "Spectral Methods and Their Applications," World Scientific Publishing Co., Inc., River Edge, NJ, 1998. |
[8] |
Ben-yu Guo, Jie Shen and Li-lian Wang, Optional spectral-Galerkin methods using generalizd Jacobi polynomials, J. Sci. Comp., 27 (2006), 305-322.
doi: 10.1007/s10915-005-9055-7. |
[9] |
Ben-yu Guo, Jie Shen and Li-lian Wang, Generalized Jacobi polynomials/functions and their applications, Appl. Numer. Math., 59 (2009), 1011-1028.
doi: 10.1016/j.apnum.2008.04.003. |
[10] |
Ben-yu Guo, Jie Shen and Zhong-qing Wang, A rational approximation and its applications to differential equations on the half line, J. Sci. Comput., 15 (2000), 117-147.
doi: 10.1023/A:1007698525506. |
[11] |
Ben-yu Guo, Jie Shen and Zhong-qing Wang, Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval, Inter. J. Numer. Meth. Engin., 53 (2002), 65-84.
doi: 10.1002/nme.392. |
[12] |
Ben-yu Guo and Li-lian Wang, Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces, J. Appr. Theo., 128 (2004), 1-41.
doi: 10.1016/j.jat.2004.03.008. |
[13] |
Ben-yu Guo and Tian-jun Wang, Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an finite channel, Math. Comp., 78 (2009), 129-151.
doi: 10.1090/S0025-5718-08-02152-2. |
[14] |
Ben-yu Guo and Tian-jun Wang, Composite Laguerre-Legendre spectral method for exterior problems, Adv. Comput. Math., 32 (2010), 393-429.
doi: 10.1007/s10444-008-9112-5. |
[15] |
Ben-yu Guo and Yong-gang Yi, Generalized Jacobi rational spectral method and its applications, J. Sci. Comput., 43 (2010), 201-238.
doi: 10.1007/s10915-010-9353-6. |
[16] |
A. B. J. Kuijlaars, A. Martinez-Finkelshtein and R. Orive, Orthogonality of Jacobi polynomials with general parameters, Elec. Tran. on Numer. Anal., 19 (2005), 1-17. |
[17] |
Li Huiyuan, "Super Spectral Viscosity Methods for Nonliear Conservation Laws, Chebyshev Collocation Methods and Their Applications," Ph.D Thesis, Shanghai University, Shanghai, China, 2002. |
[18] |
Jie Shen, Efficient spectral-Galerkin method I. Direct solvers of second- and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput., 15 (1994), 1489-1505.
doi: 10.1137/0915089. |
[19] |
Jie Shen, Efficient spectral-Galerkin method II. Direct solvers of second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comput., 16 (1995), 74-87.
doi: 10.1137/0916006. |
[20] |
Jie Shen and Li-lian Wang, Some recent advances on spectral methods for unbounded domains, Commun. Comput. Phys., 5 (2009), 195-241. |
[21] |
G. Szegö, "Orthogonal Polynomials," Amer. Math. Soc., Providence, R.I., 1959. |
[22] |
Tian-jun Wang and Zhong-qing Wang, Error analysis of Legendre spectral method with essential imposition of Neumann boundary condition, Appl. Numer. Math., 59 (2009), 2444-2451.
doi: 10.1016/j.apnum.2009.05.003. |
[23] |
Zhong-qing Wang and Ben-yu Guo, Jacobi rational approximation and spectral method for differential equations of degenerate type, Math. Comp., 77 (2008), 883-907. |
[24] |
Zhong-qing Wang and Xu-hong Yu, Jacobi spectral method with essential imposition of Neumann boundary condition, submitted. |
[25] |
Yong-gang Yi and Ben-yu Guo, Generalized Jacobi rational spectral method and its applications to degenerated differentual equations on the half line, submitted. |
show all references
References:
[1] |
F. Auteri, N. Parolini and L. Quartapelle, Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers, J. Comput. Phys., 185 (2003), 427-444.
doi: 10.1016/S0021-9991(02)00064-5. |
[2] |
J. Bergh and J. Löfström, "Interpolation Spaces. An Introduction," Grundlehren der Mathematischen Wissenschaften, No. 223, Spring-Verlag, Berlin-New York, 1976. |
[3] |
C. Bernardi and Y. Maday, Spectral Methods, in "Handbook of Numerical Analysis, Vol. V," 209-485, North-Holland, Amsterdam, 1997. |
[4] |
J. P. Boyd, Spectral method using rational basis functions on an infinite interval, J. Comp. Phys., 69 (1987), 112-142.
doi: 10.1016/0021-9991(87)90158-6. |
[5] |
J. P. Boyd, Orthogonal rational functions on a semi-infinite interval, J. Comp. Phys., 70 (1987), 63-88.
doi: 10.1016/0021-9991(87)90002-7. |
[6] |
C. I. Christov, A complete orthonormal system of functions in $L^2(-\infty,\infty)$ space, SIAM J. Appl. Math., 42 (1982), 1337-1344.
doi: 10.1137/0142093. |
[7] |
Ben-yu Guo, "Spectral Methods and Their Applications," World Scientific Publishing Co., Inc., River Edge, NJ, 1998. |
[8] |
Ben-yu Guo, Jie Shen and Li-lian Wang, Optional spectral-Galerkin methods using generalizd Jacobi polynomials, J. Sci. Comp., 27 (2006), 305-322.
doi: 10.1007/s10915-005-9055-7. |
[9] |
Ben-yu Guo, Jie Shen and Li-lian Wang, Generalized Jacobi polynomials/functions and their applications, Appl. Numer. Math., 59 (2009), 1011-1028.
doi: 10.1016/j.apnum.2008.04.003. |
[10] |
Ben-yu Guo, Jie Shen and Zhong-qing Wang, A rational approximation and its applications to differential equations on the half line, J. Sci. Comput., 15 (2000), 117-147.
doi: 10.1023/A:1007698525506. |
[11] |
Ben-yu Guo, Jie Shen and Zhong-qing Wang, Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval, Inter. J. Numer. Meth. Engin., 53 (2002), 65-84.
doi: 10.1002/nme.392. |
[12] |
Ben-yu Guo and Li-lian Wang, Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces, J. Appr. Theo., 128 (2004), 1-41.
doi: 10.1016/j.jat.2004.03.008. |
[13] |
Ben-yu Guo and Tian-jun Wang, Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an finite channel, Math. Comp., 78 (2009), 129-151.
doi: 10.1090/S0025-5718-08-02152-2. |
[14] |
Ben-yu Guo and Tian-jun Wang, Composite Laguerre-Legendre spectral method for exterior problems, Adv. Comput. Math., 32 (2010), 393-429.
doi: 10.1007/s10444-008-9112-5. |
[15] |
Ben-yu Guo and Yong-gang Yi, Generalized Jacobi rational spectral method and its applications, J. Sci. Comput., 43 (2010), 201-238.
doi: 10.1007/s10915-010-9353-6. |
[16] |
A. B. J. Kuijlaars, A. Martinez-Finkelshtein and R. Orive, Orthogonality of Jacobi polynomials with general parameters, Elec. Tran. on Numer. Anal., 19 (2005), 1-17. |
[17] |
Li Huiyuan, "Super Spectral Viscosity Methods for Nonliear Conservation Laws, Chebyshev Collocation Methods and Their Applications," Ph.D Thesis, Shanghai University, Shanghai, China, 2002. |
[18] |
Jie Shen, Efficient spectral-Galerkin method I. Direct solvers of second- and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput., 15 (1994), 1489-1505.
doi: 10.1137/0915089. |
[19] |
Jie Shen, Efficient spectral-Galerkin method II. Direct solvers of second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comput., 16 (1995), 74-87.
doi: 10.1137/0916006. |
[20] |
Jie Shen and Li-lian Wang, Some recent advances on spectral methods for unbounded domains, Commun. Comput. Phys., 5 (2009), 195-241. |
[21] |
G. Szegö, "Orthogonal Polynomials," Amer. Math. Soc., Providence, R.I., 1959. |
[22] |
Tian-jun Wang and Zhong-qing Wang, Error analysis of Legendre spectral method with essential imposition of Neumann boundary condition, Appl. Numer. Math., 59 (2009), 2444-2451.
doi: 10.1016/j.apnum.2009.05.003. |
[23] |
Zhong-qing Wang and Ben-yu Guo, Jacobi rational approximation and spectral method for differential equations of degenerate type, Math. Comp., 77 (2008), 883-907. |
[24] |
Zhong-qing Wang and Xu-hong Yu, Jacobi spectral method with essential imposition of Neumann boundary condition, submitted. |
[25] |
Yong-gang Yi and Ben-yu Guo, Generalized Jacobi rational spectral method and its applications to degenerated differentual equations on the half line, submitted. |
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