The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models

Abstract In this paper, the variational iteration method (VIM) is used to study a nonlinear singular boundary value problems arising in various physical equations. The VIM overcomes the singularity issue at the origin x  = 0. The Lagrange multipliers for all four cases of the boundary value problems are formally derived. The variational iteration method is tested for its efficiency and reliability.

[1]  G. Adomian,et al.  On the analytic solution of the lane-emden equation , 1995 .

[2]  Mehdi Dehghan,et al.  An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method , 2010, Comput. Phys. Commun..

[3]  Peng Wu,et al.  An efficient method for solving Emden-Fowler equations , 2009, J. Frankl. Inst..

[4]  V. F. Kirichenko,et al.  Substantiation of the variational iteration method in the theory of plates , 1981 .

[5]  Mehdi Dehghan,et al.  Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type , 2009, J. Comput. Phys..

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

[7]  T. Schunck.  Zur Knickfestigkeit schwach gekrümmter zylindrischer Schalen , 1933 .

[8]  A. S. V. Ravi Kanth,et al.  Cubic spline for a class of non-linear singular boundary value problems arising in physiology , 2006, Appl. Math. Comput..

[9]  Manoj Kumar,et al.  Modified Adomian Decomposition Method and computer implementation for solving singular boundary value problems arising in various physical problems , 2010, Comput. Chem. Eng..

[10]  Suheil A. Khuri,et al.  A novel approach for the solution of a class of singular boundary value problems arising in physiology , 2010, Math. Comput. Model..

[11]  M. Dehghan,et al.  Approximate solution of a differential equation arising in astrophysics using the variational iteration method , 2008 .

[12]  Abdul-Majid Wazwaz,et al.  Analytical solution for the time-dependent Emden-Fowler type of equations by Adomian decomposition method , 2005, Appl. Math. Comput..

[13]  Abdul-Majid Wazwaz,et al.  A new method for solving singular initial value problems in the second-order ordinary differential equations , 2002, Appl. Math. Comput..

[14]  M. Razzaghi,et al.  Solution of the generalized Emden–Fowler equations by the hybrid functions method , 2009 .

[15]  A. Yildirim,et al.  Solutions of singular IVPs of Lane–Emden type by the variational iteration method , 2009 .

[16]  Ahmet Yildirim,et al.  Solutions of singular IVPs of Lane–Emden type by homotopy perturbation method , 2007 .

[17]  Anjan Biswas,et al.  1-soliton solution of the K(m,n) equation with generalized evolution , 2008 .

[18]  P. Lima,et al.  Numerical modeling of oxygen diffusion in cells with Michaelis-Menten uptake kinetics , 2010 .

[19]  A. Wazwaz.  Partial Differential Equations and Solitary Waves Theory , 2009 .