A generalization of the Lane-Emden equation. (English) Zbl 1154.65059

Aslanov, Afgan

Int. J. Comput. Math. 85, No. 11, 1709-1725 (2008).

Summary: Singular initial value problems are investigated. We consider a new class of equations of Lane-Emden or Emden-Fowler type. The coefficient of \(y^\prime\) rewritten in terms of a new function \(\varphi (x)\) such that the equation can be solved in terms of \(\varphi \). Some special cases of the equation are solved as examples, to illustrate the reliableness of the method.

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

Lane-Emden equations; Emden-Fowler equations; decomposition method; numerical examples; singular initial value problems

References:

[1]	Adomian, G. 1994. ”Solving Frontier Problems of Physics: The Decomposition Method”. Boston, MA: Kluwer. · Zbl 0802.65122
[2]	Chandrasekhar, S. 1967. ”Introduction to the Study of Stellar Structure”. New York: Dover Publications.
[3]	Davis, H. T. 1962. ”Introduction to Nonlinear Differential and Integral Equations”. New York: Dover Publications.
[4]	DOI: 10.1016/S0010-4655(01)00415-5 · Zbl 0991.65065
[5]	Richardson, O. U. 1921. ”The Emission of Electricity from Hot Bodies Longman’s”. London: Green and Company.
[6]	DOI: 10.1063/1.530005 · Zbl 0780.34007
[7]	DOI: 10.1016/S0096-3003(99)00063-6 · Zbl 1028.65138
[8]	DOI: 10.1016/S0096-3003(99)00223-4 · Zbl 1023.65067
[9]	DOI: 10.1016/S0096-3003(01)00021-2 · Zbl 1030.34004
[10]	Wazwaz, A. M. 2002. ”Partial Differential Equations: Methods and Applications”. Balkema, The Netherlands
[11]	DOI: 10.1016/j.amc.2003.12.048 · Zbl 1061.65064