Solving Singular Initial Value Problems of Emden-Fowler and Lane-Emden Type

In this paper, Singular initial value problems are investigated by using Taylor series method. The solutions are constructed in the form of a convergent series. The method is applied to Emden-Fowler and Lane-Emden equations.

[1]  N. Shawagfeh Nonperturbative approximate solution for Lane–Emden equation , 1993 .

[2]  Manoj Kumar A difference method for singular two-point boundary value problems , 2003, Appl. Math. Comput..

[3]  Md. Sazzad Hossien Chowdhury,et al.  Solutions of Emden-Fowler equations by homotopy-perturbation method , 2009 .

[4]  Yahya Qaid Hasan,et al.  Solving Singular Initial Value Problems in the Second-order Ordinary Differential Equations , 2007 .

[5]  S. R. K. Iyengar,et al.  Spline finite difference methods for singular two point boundary value problems , 1986 .

[6]  H. Poincaré,et al.  Les Méthodes nouvelles de la Mécanique céleste and An Introduction to the Study of Stellar Structure , 1958 .

[7]  G. Adomian Nonlinear Stochastic Operator Equations , 1986 .

[8]  Lawrence F. Shampine,et al.  Numerical Methods for Singular Boundary Value Problems , 1975 .

[9]  Abdul-Majid Wazwaz,et al.  Adomian decomposition method for a reliable treatment of the Emden-Fowler equation , 2005, Appl. Math. Comput..

[10]  Vedat Suat Erturk,et al.  Differential Transformation Method for Solving Differential Equations of Lane-Emden Type , 2007 .

[11]  Abdul-Majid Wazwaz,et al.  A new algorithm for solving differential equations of Lane-Emden type , 2001, Appl. Math. Comput..

[12]  C. P. Katti,et al.  A Finite-difference Method for a Class of Singular Two-point Boundary-value Problems , 1984 .

[13]  M. Chawla,et al.  Orderh2 method for a singular two-point boundary value problem , 1986 .

[14]  W. Mccrea An Introduction to the Study of Stellar Structure , 1939, Nature.

[15]  H. Davis Introduction to Nonlinear Differential and Integral Equations , 1964 .

[16]  Finite difference methods for a class of singular two-point boundary-value problems , 1989 .

[17]  Salah M. El-Sayed,et al.  Multi-integral methods for nonlinear boundary-value problems , 1999, Int. J. Comput. Math..