Chebyshev spectral methods and the Lane-Emden problem

Numerical Mathematics

Volumn 4, Issue 2, 2011, Pages 142-157

  Boyd, John P ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Chebyshev polynomial; Lane Emden; Pseudospectral

Indexed keywords

EID: 80052207942     PISSN: 10048979     EISSN: 20797338     Source Type: Journal    
DOI: 10.4208/nmtma.2011.42s.2     Document Type: Article

References (28)

1. G. BASZENSKI AND F. DELVOS, Error-estimates for sine series expansions, Math. Nach., 139(1988), pp. 155-166.
2. C. M. BENDER, K. A. MILTON, S. S. PINSKY, AND L. M. SIMMONS, JR., A new perturbative approach to nonlinear problems, J. Math. Phys., 30(1989), pp. 1447-1455.
3. J. P. BOYD, A Chebyshev polynomial method for computing analytic solutions to eigenvalue problems with application to the anharmonic oscillator, J. Math. Phys., 19(1978), pp. 1445-1456.
4. -, Chebyshev and Fourier Spectral Methods, Dover, Mineola, New York, 2d ed., 2001. 665 pp. Heavily revised and updated second edition of Boyd (1989).
5. N). (Pubitemid 46195582)
6. 325, Astrophysical Journal, 89(1939), pp. 116-118.
7. -, An Introduction to the Study of Stellar Structure, Dover, New York, 1967.
8. H. T. DAVIS, Introduction to Nonlinear Differential and Integral Equations, Dover, Mineola, New York, 1962.
9. J.-H. HE, Variational approach to the Lane-Emden equation, Appl. Math. Comput., 143(2003), pp. 539-541.
10. G. P. HOREDT, 7-digit tables of Lane-Emden functions, Astrophys. Space Sci., 126(1986), pp. 357-408.
11. C. HUNTER, Series solutions for polytropes and the isothermal sphere, Month. Notic. R. Astro. Soc., 328(2001), pp. 839-847. (Pubitemid 33626907)
12. S. LIAO, A new analytic algorithm of Lane-Emden type equations, Appl. Math. Comput., 142(2003), pp. 1-16.
13. F. K. LIU, Polytropic gas spheres: An approximate analytic solution of the Lane-Emden equation, Month. Notic. R. Astro. Soc., 281(1996), pp. 1197-1205. (Pubitemid 126430673)
14. Y. L. LUKE, The Special Functions and Their Approximations, vol. I & II, Academic Press, New York, 1969.
15. -, Mathematical Functions and Their Approximations, Academic Press, New York, 1975. 566 pp.
16. V. B. MANDELZWEIG AND F. TABAKIN, Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs, Comput. Phys. Commun., 141(2001), pp. 268-281. (Pubitemid 33094166)
17. H. R. MARZBAN, H. R. TABRIZIDOOZ, AND M. RAZZAGHI, Hybrid functions for nonlinear initialvalue problems with applications to Lane-Emden type equations, Phys. Lett. A, 372(2008), pp. 5883-5886.
18. C. MOHAN AND A. R. AL-BAYATY, Power-series solutions of the Lane-Emden equation, Astrophys. Space Sci., 73(1980), pp. 227-239.
19. G. NÉMETH, Mathematical Approximation of Special Functions: Ten Papers on Chebyshev Expansions, Nova Science Publishers, New York, 1992. 200 pp.
20. M. I. NOUH, Accelerated power series solution of polytropic and isothermal gas sphe, New Astron., 9(2004), pp. 467-473.
21. K. PARAND, M. SHAHINI, AND M. DEHGAHN, Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type, J. Comput. Phys., 228(2009), pp. 8830-8840.
22. P. PASCUAL, Lane-Emden equation and Padé approximants, Astron. Astrophys., 60(1977), pp. 161-163.
23. J. I. RAMOS, Series approach to the lane-emden equation and comparison with the homotopy perturbation method, Chaos, Solitons & Fractals, 38(2008), pp. 400-408. (Pubitemid 351627012)
24. I. W. ROXBURGH AND L. M. STOCKMAN, Power series solutions of the polytrope equations, Mon. Not. R. Astron. Soc., 4303(1999), pp. 466-470.
25. D. H. SADLER AND J. C. P. MILLER, Tables of the Lane-Emden function, in Mathematical Tables, vol. 2, Office of the British Association, London, 1932.
26. N. T. SHAWAGFEH, Nonperturbative approximate solution for Lane-Emden equation, J. Math. Phys., 34(1993), pp. 3867-4372.
27. V. B. SHEOREY, Double Chebyshev expansions for wave functions, Comput. Phys. Commun., 12(1976), pp. 125-134.
28. A. YILDIRIM AND T. ÖZIŞ, Solutions of singular IVPs of Lane-Emden type by the variational iteration method, Nonlinear Analysis, 70(2009), pp. 2480-2484.