The use of He's variational iteration method for solving the telegraph and fractional telegraph equations

In this paper the variational iteration method is used to compute the solution for the linear, variable coefficient, fractional derivative and multi space telegraph equations. The method constructs a convergent sequence of functions, to approximate the exact solution with a few number of iterations without discretization. Numerical results and comparison with exact solutions are given for some examples in order to show its applicability and efficiency. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Saeid Abbasbandy,et al.  Numerical method for non‐linear wave and diffusion equations by the variational iteration method , 2008 .

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

[3]  Mehdi Dehghan,et al.  Numerical solution of the Klein–Gordon equation via He’s variational iteration method , 2007 .

[4]  Mehdi Dehghan,et al.  Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method , 2008 .

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

[6]  Saeid Abbasbandy,et al.  The Variational Iteration Method for a Class of Eighth-Order Boundary-Value Differential Equations , 2008 .

[7]  Mehdi Dehghan,et al.  High order implicit collocation method for the solution of two‐dimensional linear hyperbolic equation , 2009 .

[8]  R. K. Mohanty.  An operator splitting technique for an unconditionally stable difference method for a linear three space dimensional hyperbolic equation with variable coefficients , 2005, Appl. Math. Comput..

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

[10]  Mehdi Dehghan,et al.  Variational iteration method for solving a generalized pantograph equation , 2009, Comput. Math. Appl..

[11]  Shaher Momani,et al.  Analytic and approximate solutions of the space- and time-fractional telegraph equations , 2005, Appl. Math. Comput..

[12]  Mehdi Dehghan,et al.  Numerical solution of a biological population model using He's variational iteration method , 2007, Comput. Math. Appl..

[13]  Mehdi Dehghan,et al.  Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method , 2010 .

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

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

[16]  Mehdi Dehghan,et al.  Solution of a model describing biological species living together using the variational iteration method , 2008, Math. Comput. Model..

[17]  Mehdi Dehghan,et al.  Improvement of He's variational iteration method for solving systems of differential equations , 2009, Comput. Math. Appl..

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

[19]  M. Dehghan,et al.  Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem , 2008 .

[20]  Mehdi Dehghan,et al.  The use of He's variational iteration method for solving variational problems , 2010, Int. J. Comput. Math..

[21]  Mehdi Dehghan,et al.  The use of He's variational iteration method for solving a Fokker–Planck equation , 2006 .

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

[23]  Jacek Banasiak,et al.  Singularly perturbed telegraph equations with applications in the random walk theory , 1998 .

[24]  S. Abbasbandy,et al.  Application of the Variational Iteration Method for System of Nonlinear Volterra’s Integro-Differential Equations , 2009 .

[25]  M. Dehghan,et al.  The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics , 2008 .

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

[27]  Saeid Abbasbandy,et al.  Application of the Variational Iteration Method to Nonlinear Volterra’s Integro-Differential Equations , 2008 .

[28]  Mehdi Dehghan,et al.  Variational iteration method for solving the wave equation subject to an integral conservation condition , 2009 .

[29]  Mehdi Dehghan,et al.  On the convergence of He's variational iteration method , 2007 .

[30]  Sailing He,et al.  Wave splitting of the telegraph equation in R3 and its application to inverse scattering , 1993 .

[31]  Mehdi Dehghan,et al.  Solving a fourth‐order fractional diffusion‐wave equation in a bounded domain by decomposition method , 2008 .

[32]  M. Dehghan,et al.  The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique , 2009 .

[33]  Feng Gao,et al.  Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation , 2007, Appl. Math. Comput..

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

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

[36]  Mehdi Dehghan,et al.  High order compact solution of the one‐space‐dimensional linear hyperbolic equation , 2008 .

[37]  Mehdi Dehghan,et al.  Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices , 2006, Math. Comput. Simul..

[38]  Shaher Momani,et al.  Numerical approach to differential equations of fractional order , 2007 .

[39]  M. Dehghan,et al.  Solution of problems in calculus of variations via He's variational iteration method , 2007 .

[40]  Ji-Huan He,et al.  Construction of solitary solution and compacton-like solution by variational iteration method , 2006 .

[41]  Mehdi Dehghan,et al.  Solution of parabolic integro‐differential equations arising in heat conduction in materials with memory via He's variational iteration technique , 2010 .

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

[43]  Mehdi Dehghan,et al.  The use of Chebyshev cardinal functions for solution of the second‐order one‐dimensional telegraph equation , 2009 .

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

[45]  Abdul-Majid Wazwaz,et al.  The variational iteration method for a reliable treatment of the linear and the nonlinear Goursat problem , 2007, Appl. Math. Comput..

[46]  Mehdi Dehghan,et al.  A numerical method for solving the hyperbolic telegraph equation , 2008 .

[47]  Ashok Puri,et al.  Digital signal propagation in dispersive media. , 1999 .

[48]  Lucas Jódar,et al.  Computing the variable coefficient telegraph equation using a discrete eigenfunctions method , 2007, Comput. Math. Appl..