Application of the BPES to Lane-Emden equations governing polytropic and isothermal gas spheres

New Astronomy

Volumn 17, Issue 6, 2012, Pages 565-569

  Boubaker, K ^a   Van Gorder, Robert A ^b  

^a FACULTÉ DES SCIENCES DE TUNIS   (Tunisia)

^b UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Analytical methods; Lane Emden equations; Stellar interiors

Indexed keywords

EID: 84857985238     PISSN: 13841076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.newast.2012.02.003     Document Type: Article

References (39)

1. Emden, R., 1907. Gaskugeln Anwendungen der Mechan. Warmtheorie, Druck und Verlag Von B.G. Teubner, Leipzig and Berlin.
2. J.H. Lane American Journal of Science and Arts 50 1870 57
3. W.B. Bonnor Boyle's law and gravitational instability MNRAS 116 1956 351
4. R. Ebert Uber die Verdichtung von H I-Gebieten Zeitschrift fur Astrophysik 37 1955 217
5. J. Binney, and S. Tremaine Glactic Dynamics 1987 Princeton University Press Princeton
6. R. Kippenhahn, and A. Weigert Stellar Structure and Evolution 1990 Springer Berlin
7. R.A. Van Gorder Analytical solutions to a quasilinear differential equation related to the Lane-Emden equation of the second kind Celestial Mechanics and Dynamical Astronomy 109 2011 137 145
8. S. Chandrasekhar An Introduction to the Study of Stellar Structure 1667 Dover New York p.90
9. A.M. Wazwaz A new algorithm for solving differential equations of Lane-Emden type Applied Mathematics and Computation 118 2001 287 310
10. C. Hunter Series solutions for polytropes and the isothermal sphere Monthly Notices of the Royal Astronomical Society 328 2001 839 847 (Pubitemid 33626907)
11. B.M. Mirza Approximate analytical solutions of the Lane-Emden equation for a self-gravitating isothermal gas sphere Monthly Notices of the Royal Astronomical Society 395 2009 2288 2291
12. R.A. Van Gorder An elegant perturbation solution for the Lane-Emden equation of the second kind New Astronomy 16 2011 65 67
13. A. Yildirim, and T. Ozis Solutions of singular IVPs of Lane-Emden type by the variational iteration method Nonlinear Analysis: Theory Methods and Applications 70 2009 2480 2484
14. A.M. Wazwaz The variational iteration method for solving systems of equations of Emden-Fowler type International Journal of Computer Mathematics 2011 doi:10.1080/00207160.2011.587513
15. S. Iqbal, and A. Javed Application of optimal homotopy asymptotic method for the analytic solution of singular Lane-Emden type equation Applied Mathematics and Computation 217 2011 7753 7761
16. R.A. Van Gorder, and K. Vajravelu Analytic and numerical solutions to the Lane-Emden equation Physics Letters A 372 2008 6060 6065
17. K. Parand, S. Abbasbandy, S. Kazem, and A.R. Rezaei An improved numerical method for a class of astrophysics problems based on radial basis functions Physica Scripta 83 2011 015011
18. C.M. Khalique, and P. Ntsime Exact solutions of the Lane-Emden-type equation New Astronomy 13 2008 476 480
19. K. Parand, A.R. Rezaei, and A. Taghavi Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domains Acta Astronautica 67 2010 673 680
20. Yang, C., Hou, J., 2010. A numerical method for Lane-Emden equations using Chebyshev polynomials and the collocation method. In: IEEE 2010 International Conference on Computational and Information Sciences, pp. 97-100.
21. A.H. Bhrawy, and A.S. Alofi A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations Communications in Nonlinear Science and Numerical Simulation 17 2012 62 70
22. M.I. Nouh Accelerated power series solution of polytropic and isothermal gas spheres New Astronomy 9 2004 467 473
23. E. Momoniat, and C. Harley Approximate implicit solution of a Lane-Emden equation New Astronomy 11 2006 520 526
24. C. Harley, and E. Momoniat First integrals and bifurcations of a Lane-Emden equation of the second kind Journal of Mathematical Analysis and Application 344 2008 757 764
25. H. Goenner, and P. Havas Exact solutions of the generalized Lane-Emden equation Journal of Mathematical Physics 41 2000 7029 7042
26. R.A. Van Gorder Exact first integrals for a Lane-Emden equation of the second kind modeling a thermal explosion in a rectangular slab New Astronomy 16 2011 492 497
27. A. Belhadj, O. Onyango, and N. Rozibaeva Boubaker polynomials expansion scheme-related heat transfer investigation inside Keyhole model Journal of Thermophysics and Heat Transfer 23 2009 639 642
28. A.S. Kumar An analytical solution to applied mathematics-related love's equation using the Boubaker polynomials expansion scheme Journal of the Franklin Institute 347 2010 1755 1761
29. A. Belhadj, J. Bessrour, M. Bouhafs, and L. Barrallier Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion Journal of Thermal Analysis and Calorimetry 97 2009 911 920
30. P. Barry, and A. Hennessy Meixner-Type results for Riordan arrays and associated integer sequences, section 6: the Boubaker polynomials Journal of Integer Sequences 13 2010 1 34
31. M. Agida, and A.S. Kumar Boubaker polynomials expansion scheme solution to random love equation in the case of a rational kernel Journal of Theoretical Physics 7 2010 319 326
32. A. Yildirim, S.T. Mohyud-Din, and D.H. Zhang Analytical solutions to the pulsed Klein-Gordon equation using modified variational iteration method (MVIM) and Boubaker polynomials expansion scheme (BPES) Computers and Mathematics with Applications 2010 doi:0.1016/j.camwa.2009.12.026
33. J. Ghanouchi, H. Labiadh, and K. Boubaker An attempt to solve the heat transfert equation in a model of pyrolysis spray using 4q-order m-Boubaker polynomials International Journal of Heat and Technology 26 2008 49 53
34. O.B. Awojoyogbe, and K. Boubaker A solution to Bloch NMR flow equations for the analysis of homodynamic functions of blood flow system using m-Boubaker polynomials Current Applied Physics 9 2009
35. S. Slama, J. Bessrour, M. Bouhafs, and K.B. Ben Mahmoud Numerical Heat Transfer Part A 55 2009 401 404
36. S. Slama, M. Bouhafs, and K.B. Ben Mahmoud A Boubaker polynomials solution to heat equation for monitoring A3 point evolution during resistance spot welding International Journal of Heat and Technology 26 2 2008 141 146
37. S. Tabatabaei, T. Zhao, O. Awojoyogbe, and F. Moses Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme International Journal Heat Mass Transfer 45 2009 1247 1255
38. S. Fridjine, and M. Amlouk A new parameter: an abacus for optimizig functional materials using the Boubaker polynomials expansion scheme Modern Physics Letter B 23 2009 2179 2182
39. A. Milgram The stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka-Volterra problem Journal of Theoretical Biology 271 2011 157 158