Some solutions of the linear and nonlinear Klein-Gordon equations using the optimal homotopy asymptotic method

Abstract We investigate the effectiveness of the Optimal Homotopy Asymptotic Method (OHAM) in solving time dependent partial differential equations. To this effect we consider the homogeneous, non-homogeneous, linear and nonlinear Klein–Gordon equations with boundary conditions. The results reveal that the method is explicit, effective, and easy to use.

[1]  Ji-Huan He,et al.  A Modified Perturbation Technique Depending Upon an Artificial Parameter , 2000 .

[2]  Abdul-Majid Wazwaz,et al.  The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation , 2005, Appl. Math. Comput..

[3]  Elias Deeba,et al.  A Decomposition Method for Solving the Nonlinear Klein-Gordon Equation , 1996 .

[4]  Abdul Majeed Siddiqui,et al.  Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method , 2008 .

[5]  N. Herisanu,et al.  Optimal homotopy asymptotic method with application to thin film flow , 2008 .

[6]  Abdul-Majid Wazwaz,et al.  The modified decomposition method for analytic treatment of differential equations , 2006, Appl. Math. Comput..

[7]  Nicolae Herisanu,et al.  An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate , 2009, Appl. Math. Lett..

[8]  John D. Gibbon,et al.  The sine-Gordon equation as a model classical field theory , 1975 .

[9]  Vasile Marinca,et al.  A NEW ANALYTICAL APPROACH TO NONLINEAR VIBRATION OF AN ELECTRICAL MACHINE , 2008 .

[10]  Ji-Huan He.  Periodic solutions and bifurcations of delay-differential equations , 2005 .

[11]  Davood Domiri Ganji,et al.  Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method , 2006 .

[12]  Salah M. El-Sayed,et al.  The decomposition method for studying the Klein–Gordon equation , 2003 .

[13]  Ji-Huan He.  An approximate solution technique depending on an artificial parameter: A special example , 1998 .

[14]  N. Herisanu,et al.  Application of Optimal Homotopy Asymptotic Method for solving nonlinear equations arising in heat transfer , 2008 .

[15]  S. Liao,et al.  Application of Homotopy Analysis Method in Nonlinear Oscillations , 1998 .