Application of variational iteration method to heat- and wave-like equations

In this Letter, variational iteration method (VIM) is employed to obtain analytical solution for the heat- and wave-like equations with singular behaviors. Comparisons with the exact solution show that the VIM is a powerful method for the solution of linear and nonlinear singular equations.

[1]  A. A. Soliman,et al.  Variational iteration method for solving Burger's and coupled Burger's equations , 2005 .

[2]  A. Wazwaz.  The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations , 2007 .

[3]  Mohammad Mahdi Hosseini,et al.  On the convergence of Adomian decomposition method , 2006, Appl. Math. Comput..

[4]  M. Moghimi,et al.  Variational iteration method for solving generalized Burger–Fisher and Burger equations , 2007 .

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

[6]  Tamer A. Abassy,et al.  Toward a modified variational iteration method , 2007 .

[7]  A. Wazwaz.  A comparison between the variational iteration method and Adomian decomposition method , 2007 .

[8]  Ji-Huan He,et al.  A simple perturbation approach to Blasius equation , 2003, Appl. Math. Comput..

[9]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

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

[11]  Ji-Huan He,et al.  An iteration formulation for normalized diode characteristics , 2004, Int. J. Circuit Theory Appl..

[12]  Shijun Liao,et al.  A new analytic algorithm of Lane-Emden type equations , 2003, Appl. Math. Comput..

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

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

[15]  Dimitrios E. Panayotounakos,et al.  Exact analytic solutions of unsolvable classes of first- and second-order nonlinear ODEs (Part II: Emden-Fowler and relative equations) , 2005, Appl. Math. Lett..

[16]  M. A. Abdou,et al.  The solution of nonlinear coagulation problem with mass loss , 2006 .

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

[18]  Ebrahim Momoniat,et al.  APPROXIMATE IMPLICIT SOLUTION OF A LANE-EMDEN EQUATION , 2006 .

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

[20]  Junfeng Lu,et al.  Variational iteration method for solving two-point boundary value problems , 2007 .

[21]  Ji-Huan He.  Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[22]  Necdet Bildik,et al.  The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations , 2006 .

[23]  Shaher Momani,et al.  Application of He’s variational iteration method to Helmholtz equation , 2006 .

[24]  Ji-Huan He.  A new approach to nonlinear partial differential equations , 1997 .

[25]  A. A. Soliman,et al.  A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations , 2006 .

[26]  Ishak Hashim,et al.  Numerical simulation of the generalized Huxley equation by He's variational iteration method , 2007, Appl. Math. Comput..

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

[28]  Ji-Huan He.  Approximate analytical solution of Blasius' equation , 1998 .

[29]  Ji-Huan He.  SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[30]  S. Abbasbandy.  A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials , 2007 .

[31]  Ji-Huan He.  Variational approach to the Lane-Emden equation , 2003, Appl. Math. Comput..

[32]  Sohrabali Yousefi,et al.  Legendre wavelets method for solving differential equations of Lane-Emden type , 2006, Appl. Math. Comput..

[33]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..