Approximate solutions of Emden-Fowler type equations

International Journal of Computer Mathematics

Volumn 86, Issue 5, 2009, Pages 807-826

  Aslanov, Afgan ^a  

^a FATIH UNIVERSITY   (Turkey)

Author keywords

Emden Fowler equations; Initial value problems; Lane Emden equations; decomposition method; Singularity

Indexed keywords

APPROXIMATE SOLUTION; CONVERGENT SERIES; DECOMPOSITION METHODS; EMDEN-FOWLER EQUATIONS; SINGULARITY;

COMPUTER SCIENCE; MATHEMATICAL TECHNIQUES;

INITIAL VALUE PROBLEMS;

EID: 67651176132     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160701708235     Document Type: Article

References (20)

1. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, MA, 1994.
2. C.V. Bender, K.A. Milton, S.S. Pinsky, and L.M. Simmons, A new perturbative approach to nonlinear problems, J. Math. Phys. 30 (1989), pp. 1447-1455.
3. J. Binney and S. Tremaine, Glastic Dynamics, Princeton University Press, Princeton, 1987.
4. W.B. Bonnor, Boyle's law and gravitational instability. MNRAS 116 (1956), p. 351,
5. S. Chandrasekhar, Introduction to the Study of Stellar Structure, Dover Publications, New York, 1967.
6. H.T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, 1962.
7. R. Kippenhahn and A. Weigert, Stellar Structure and Evolution, Springer, Berlin, 1990.
8. S. Liao, A new analytic algorithm of Lane - Emden type equations, Appl. Math. Comput. 142 (2003), pp. 1-16.
9. C.D. Luning and W.L. Perry, Positive solutions of negative exponent generalized Emden - Fowler boundary value problems, SIAM J. Math. Anal. 12(6) (1981), pp. 874-879.
10. 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
11. O.U. Richardson, The Emission of Electricity from Hot Bodies, Longman's Green and Company, London, 1921.
12. N.T. Shawagfeh, Nonperturbative approximate solution for Lane - Emden equations, J. Math. Phys. 34(9) (1993), p. 4364.
13. B.D. Vujanovic, A.M. Strauss, S.E. Jones, and P.P. Gillis, Polynomial conservation laws of the generalized Emden-Fowler equation, Int. J. Non-linear Mech. 33(2) (1998), pp. 377-384.
14. A.M. Wazwaz, A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. Math. Comput. 111(1) (2000), pp. 33-51
15. A.M. Wazwaz, A new algorithm for solving differential equations of Lane - Emden type, Appl. Math. Comput. 118 (2001), pp. 287-310
16. A.M. Wazwaz, A new method for solving singular value problem in the second order ordinary differential equations, Appl. Math. Comput. 128 (2002), pp. 45-57.
17. A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, The Netherlands, 2002
18. A.M. Wazwaz, Adomian decomposition method for a reliable treatment of the Emden - Fowler equation, Appl. Math. Comput. 161 (2005), pp. 543-560
19. J.S.W. Wong, On the generalized Emden - Fowler equation, SIAM Rev. 17(2) (1975), pp. 339-360.
20. V.F. Zaitsev and A.D. Polyanin, Discrete Group Methods for Integrating Equations of Nonlinear Mechanics, CRC Press, Florida, 1994.