Variational iteration method for solving nonlinear boundary value problems

Abstract In this paper, He’s variational iteration method is implemented to give approximate and analytical solutions for a class of boundary value problems. The variational iteration method, which produces the solutions in terms of convergent series, requiring no linearization or small perturbation. Numerical examples are given and comparisons are made with the Adomian decomposition method. The fact that this method solves nonlinear equations without using Adomian polynomials can be considered as an advantage of this method over Adomian decomposition method.

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

[2]  H. Sekine,et al.  General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics1 , 1980 .

[3]  Tian-Hu Hao,et al.  Search for Variational Principles in Electrodynamics by Lagrange Method , 2005 .

[4]  S. Momani,et al.  Analytical approach to linear fractional partial differential equations arising in fluid mechanics , 2006 .

[5]  Ji-Huan He.  Approximate analytical solution for seepage flow with fractional derivatives in porous media , 1998 .

[6]  Ji-Huan He,et al.  Variational iteration method for delay differential equations , 1997 .

[7]  S. M. Roberts,et al.  On the closed form solution of Troesch's problem , 1976 .

[8]  Ji-Huan He,et al.  Semi-Inverse Method of Establishing Generalized Variational Principles for Fluid Mechanics With Emphasis on Turbomachinery Aerodynamics , 1997 .

[9]  A. Wazwaz.  A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems , 2001 .

[10]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[11]  Ji-Huan He,et al.  Variational Principle for Nano Thin Film Lubrication , 2003 .

[12]  S. Khuri,et al.  An Algorithm for Solving Boundary Value Problems , 2000 .

[13]  Abdou,et al.  VARIATIONAL ITERATION METHOD FOR SOLVING BURGERS AND COUPLED BURGERS EQUATIONS , 2005 .

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

[15]  B. A Troesch,et al.  A simple approach to a sensitive two-point boundary value problem , 1976 .

[16]  V. Marinca,et al.  An Approximate Solution for One-Dimensional Weakly Nonlinear Oscillations , 2002 .

[17]  Ji-Huan He,et al.  Variational principles for some nonlinear partial differential equations with variable coefficients , 2004 .

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

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

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

[21]  Ji-Huan He,et al.  Variational Theory for Linear Magneto-Electro-Elasticity , 2001 .

[22]  Ji-Huan He.  Approximate solution of nonlinear differential equations with convolution product nonlinearities , 1998 .

[23]  Hong-Mei Liu,et al.  Variational Approach to Nonlinear Electrochemical System , 2004 .

[24]  G. Drăgănescu,et al.  Nonlinear Relaxation Phenomena in Polycrystalline Solids , 2003 .

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

[26]  Hong-Mei Liu,et al.  Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method , 2005 .

[27]  S. Momani,et al.  Numerical comparison of methods for solving linear differential equations of fractional order , 2007 .