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Laguerre spectral method with different basis functions

Year 2015, Volume: 36 Issue: 3, 876 - 880, 13.05.2015

Ali Baderan , Hadi Darvıshı Morteza Mohammad Nezhad Kıasary

Abstract

Abstract. In this paper a model has been solved using Laguerre spectral method with two different basis functions. Unlike classical method, all the boundary conditions will be satisfied using linear combination of Laguerre functions as basis functions. Numerical results show that using a new basis has less error and also leads to three diagonal matrix that has a conditions number which is smaller than that of the classical method. 

Keywords

Linear differential equations Basis functions Combination of Laguerre functions Laguerre spectral method

References

  • C. Bernardi, Y. Maday, Spectral method, in:P.G. Ciarlet, j. L. Lions (Eds.), Handbook of Numerical Analysis, Elsevier, Amsterdam, 1997, pp. 209-486.
  • C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods, Springer-Verlag, Berlin, 2006.
  • O. Coulaud, D. Funaro, O. Kavian, em Laguerre spectral approximation of elliptic problems in exterior domains, Comput. Methods Appl. Mech. Engrg. 80,(1990) 451–458.
  • D. Funaro, Computational aspects of pseudospectral Laguerre approximations, Appl. Numer. Math. 6 (1990) 447–457.
  • Ben-yu Guo, Spectral Methods and their Applications, World Scientific, Singapore 1998.
  • Ben-yu Guo, He-ping Ma, Composite Legendre–Laguerre approximation in unbounded domains, J. Comput. Math. 19 (2001) 101–112.
  • Ben-yu Guo, Shen Jie, Laguerre–Galerkin method for nonlinear partial differential equations on a semi-infinite interval, Numer. Math. 86 (2000).
  • Ben-yu Guo, Shen Jie, Cheng-Long Xu, Generalized Laguerre approximation and its applications to exterior problems, J. Comput. Math. 23 (2005)113–130.
  • Ben-yu Guo, Li-lian Wang, Zhong-qing Wang, Generalized Laguerre interpolation and pseudospectral method for unbounded domains, SIAM J. Numer.Anal. 43 (2006) 2567–2589.
  • Ben-yu Guo, Cheng-long Xu, Mixed Laguerre–Legendre pseudospectral method for incompressible fluid flow in an infinite strip, Math. Comp. 72(2003) 95–125.
  • Ben-yu Guo, Xiao-yong Zhang, A new generalized Laguerre approximation and its applications, J. Comput. Appl. Math. 181 (2005) 342–363.
  • He-ping Ma, Ben-yu Guo, Composite Legendre–Laguerre pseudospectral approximation in unbounded domains, IMA J. Numer. Anal. 21 (2001)587–602.
  • Shen Jie, Stable and efficient spectral methods in unbounded domains using Laguerre functions, SIAM J. Numer. Anal. 38 (2000) 1113–1133.
  • Zhong-qing Wang, Ben-yu Guo, Yan-na Wu, Pseudospectral method using generalized Laguerre functions for singular problems on unboundeddomains, Discrete Contin. Dyn. Syst. Ser. B 11 (2009) 1019–1038.
  • Cheng-long Xu, Ben-yu Guo, Mixed Laguerre–Legendre spectral method for incompressible fluid flow in an infinite strip, Adv. Comput. Math. 16 (2002)77–96.
  • Cheng-long Xu, Ben-yu Guo, Laguerre pseudospectral method for nonlinear partial differential equation, J. Comput. Math. 20 (2002) 413–428.
  • Wang Zhong-qing, The Laguerre spectral method for solving Neumann boundary Value problems, Journal of Computational and Applied Mathematics, 235(2011), 3229– 32
  • Jie Shen, Tao Tang, Li-Lian Wang, Spectral Methods,Algorithms, Analysis and Applications, Springer-Verlag Berlin Heidelberg. 2011. ou uy -neBoyuBa nliBa, o enugih qeulyg yg ga egeBuaih emuiuayBe y geaeBegiue ,ou uy -t uo e 0o ueaBa aeBegihaNeg piauegge uBnuayBe, g h. zuqeg. eiul. t1 y 1pyt. y17t -oaiy

Year 2015, Volume: 36 Issue: 3, 876 - 880, 13.05.2015

Ali Baderan , Hadi Darvıshı Morteza Mohammad Nezhad Kıasary

Abstract

References

  • C. Bernardi, Y. Maday, Spectral method, in:P.G. Ciarlet, j. L. Lions (Eds.), Handbook of Numerical Analysis, Elsevier, Amsterdam, 1997, pp. 209-486.
  • C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods, Springer-Verlag, Berlin, 2006.
  • O. Coulaud, D. Funaro, O. Kavian, em Laguerre spectral approximation of elliptic problems in exterior domains, Comput. Methods Appl. Mech. Engrg. 80,(1990) 451–458.
  • D. Funaro, Computational aspects of pseudospectral Laguerre approximations, Appl. Numer. Math. 6 (1990) 447–457.
  • Ben-yu Guo, Spectral Methods and their Applications, World Scientific, Singapore 1998.
  • Ben-yu Guo, He-ping Ma, Composite Legendre–Laguerre approximation in unbounded domains, J. Comput. Math. 19 (2001) 101–112.
  • Ben-yu Guo, Shen Jie, Laguerre–Galerkin method for nonlinear partial differential equations on a semi-infinite interval, Numer. Math. 86 (2000).
  • Ben-yu Guo, Shen Jie, Cheng-Long Xu, Generalized Laguerre approximation and its applications to exterior problems, J. Comput. Math. 23 (2005)113–130.
  • Ben-yu Guo, Li-lian Wang, Zhong-qing Wang, Generalized Laguerre interpolation and pseudospectral method for unbounded domains, SIAM J. Numer.Anal. 43 (2006) 2567–2589.
  • Ben-yu Guo, Cheng-long Xu, Mixed Laguerre–Legendre pseudospectral method for incompressible fluid flow in an infinite strip, Math. Comp. 72(2003) 95–125.
  • Ben-yu Guo, Xiao-yong Zhang, A new generalized Laguerre approximation and its applications, J. Comput. Appl. Math. 181 (2005) 342–363.
  • He-ping Ma, Ben-yu Guo, Composite Legendre–Laguerre pseudospectral approximation in unbounded domains, IMA J. Numer. Anal. 21 (2001)587–602.
  • Shen Jie, Stable and efficient spectral methods in unbounded domains using Laguerre functions, SIAM J. Numer. Anal. 38 (2000) 1113–1133.
  • Zhong-qing Wang, Ben-yu Guo, Yan-na Wu, Pseudospectral method using generalized Laguerre functions for singular problems on unboundeddomains, Discrete Contin. Dyn. Syst. Ser. B 11 (2009) 1019–1038.
  • Cheng-long Xu, Ben-yu Guo, Mixed Laguerre–Legendre spectral method for incompressible fluid flow in an infinite strip, Adv. Comput. Math. 16 (2002)77–96.
  • Cheng-long Xu, Ben-yu Guo, Laguerre pseudospectral method for nonlinear partial differential equation, J. Comput. Math. 20 (2002) 413–428.
  • Wang Zhong-qing, The Laguerre spectral method for solving Neumann boundary Value problems, Journal of Computational and Applied Mathematics, 235(2011), 3229– 32
  • Jie Shen, Tao Tang, Li-Lian Wang, Spectral Methods,Algorithms, Analysis and Applications, Springer-Verlag Berlin Heidelberg. 2011. ou uy -neBoyuBa nliBa, o enugih qeulyg yg ga egeBuaih emuiuayBe y geaeBegiue ,ou uy -t uo e 0o ueaBa aeBegihaNeg piauegge uBnuayBe, g h. zuqeg. eiul. t1 y 1pyt. y17t -oaiy
There are 18 citations in total.

Details

Journal Section Special
Authors

Ali Baderan

Hadi Darvıshı This is me

Morteza Mohammad Nezhad Kıasary This is me

Publication Date May 13, 2015
Published in Issue Year 2015 Volume: 36 Issue: 3

Cite

APA Baderan, A., Darvıshı, H., & Mohammad Nezhad Kıasary, M. (2015). Laguerre spectral method with different basis functions. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 36(3), 876-880.
AMA Baderan A, Darvıshı H, Mohammad Nezhad Kıasary M. Laguerre spectral method with different basis functions. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. May 2015;36(3):876-880.
Chicago Baderan, Ali, Hadi Darvıshı, and Morteza Mohammad Nezhad Kıasary. “Laguerre Spectral Method With Different Basis Functions”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36, no. 3 (May 2015): 876-80.
EndNote Baderan A, Darvıshı H, Mohammad Nezhad Kıasary M (May 1, 2015) Laguerre spectral method with different basis functions. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36 3 876–880.
IEEE A. Baderan, H. Darvıshı, and M. Mohammad Nezhad Kıasary, “Laguerre spectral method with different basis functions”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, pp. 876–880, 2015.
ISNAD Baderan, Ali et al. “Laguerre Spectral Method With Different Basis Functions”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36/3 (May 2015), 876-880.
JAMA Baderan A, Darvıshı H, Mohammad Nezhad Kıasary M. Laguerre spectral method with different basis functions. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36:876–880.
MLA Baderan, Ali et al. “Laguerre Spectral Method With Different Basis Functions”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, 2015, pp. 876-80.
Vancouver Baderan A, Darvıshı H, Mohammad Nezhad Kıasary M. Laguerre spectral method with different basis functions. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36(3):876-80.