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A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

  • Zhong-Qing Wang (a1) and Jun Mu (a1)

We introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain the hp-version bound on the numerical error of the multiple interval collocation method under H1-norm. Numerical experiments confirm the theoretical expectations.

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*Corresponding author. Email (Z.-Q. Wang), (J. Mu)
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[1] P. Z. Bar-Yoseph , D. Fisher and O. Gottlieb , Spectral element methods for nonlinear spatio-temporal dynamics of an Euler-Bernoulli beam, Comput. Mech., vol. 19, no. 2 (1996), pp. 136151.

[2] P. Z. Bar-Yoseph and E. Moses , Space-time spectral element methods for unsteady convection-diffusion problems, Int. J. Numer. Methods for Heat & Fluid Flow, vol. 7, no. 2-3 (1997), pp. 215235.

[3] C. Bernardi and Y. Maday , Spectral method, in Handbook of Numerical Analysis, vol. 5, 209485, edited by P. G. Ciarlet and J. L. Lions , North-Holland, Amsterdam, 1997.

[7] P. Dutt , Spectral methods for initial-boundary value problems-an alternative approach, SIAM J. Numer. Anal., vol. 27, no. 4 (1990), pp. 885903.

[10] B.-Y. Guo , Spectral Methods and Their Applications, World Scientific, Singapore, 1998.

[11] B.-Y. Guo and Z.-Q. Wang , Legendre-Gauss collocation methods for ordinary differential equations, Adv. Comput. Math., vol. 30, no. 3 (2009), pp. 249280.

[12] B.-Y. Guo and Z.-Q. Wang , A spectral collocationmethod for solving initial value problems of first order ordinary differential equations, Discrete Contin. Dyn. Syst. Ser. B, vol. 14, no. 3 (2010), pp. 10291054.

[14] B.-Y. Guo , Z.-Q. Wang , H.-J. Tian and L.-L. Wang , Integration processes of ordinary differential equations based on Laguerre-Radau interpolations, Math. Comp., vol. 77, no. 261 (2008), pp. 181199.

[15] B.-Y. Guo and J.-P. Yan , Legendre-Gauss collocation methods for initial value problems of second order ordinary differential equations, Appl. Numer. Math., vol. 59, no. 6 (2009), pp. 13861408.

[17] G. Ierley , B. Spencer and R. Worthing , Spectral methods in time for a class of parabolic partial differential equations, J. Comput. Phys., vol. 102, no. 1 (1992), pp. 8897.

[19] H.-P. Ma , Chebyshev-Legendre spectral viscosity method for nonlinear conservation laws, SIAM J. Numer. Anal., vol. 35, no. 3 (1998), pp. 869892.

[20] B. De Maerschalck and M. I. Gerritsma , The use of Chebyshev polynomials in the space-time least-squares spectral element method, Numer. Algorithms, vol. 38, (2005), pp. 173196.

[22] H. Tal-Ezer , Spectral methods in time for hyperbolic equations, SIAM J. Numer. Anal., vol. 23, no. 1 (1986), pp. 1126.

[23] H. Tal-Ezer , Spectral methods in time for parabolic problems, SIAM J. Numer. Anal., vol. 26, no. 1 (1989), pp. 111.

[25] J.-G. Tang and H.-P. Ma , A Legendre spectral method in time for first-order hyperbolic equations, Appl. Numer. Math., vol. 57, no. 1 (2007), pp. 111.

[26] Z.-Q. Wang and B.-Y. Guo , Legendre-Gauss-Radau collocation methods for solving initial value problems of first order ordinary differential equations, J. Sci. Comput., vol. 52, no. 1 (2012), pp. 226255.

[27] Z.-Q. Wang and L.-L. Wang , A Legendre-Gauss collocation method for nonlinear delay differential equations, Discrete Contin. Dyn. Syst. Ser. B, vol. 13, no. 3 (2010), pp. 685708.

[30] X. Yang and Z.-Q. Wang , A Chebyshev-Gauss spectral collocation method for ordinary differential equations, J. Comput. Math., vol. 33, no. 1 (2015), pp. 5985.

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Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
  • URL: /core/journals/numerical-mathematics-theory-methods-and-applications
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