A Reliable Treatment of Homotopy Perturbation Method for Solving the Nonlinear Klein-Gordon Equation of Arbitrary (Fractional) Orders

A Reliable Treatment of Homotopy Perturbation Method for Solving the Nonlinear Klein-Gordon Equation of Arbitrary (Fractional) Orders

A Reliable Treatment of Homotopy Perturbation Method for the Sine-gordon Equation of Arbitrary (fractional) Order

In this paper, the reliable treatment of homotopy perturbation method (HPM) [19] is applied to obtain the solution of the sine-Gordon partial di¤erential equation of arbitrary (fractional) order. The advantage of this algorithm is its ability to provide the analytical or approximate solutions to nonlinear equations with the capability to overcome the di¢ culty that arises in calculating complic...

SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

Homotopy perturbation method for solving fractional Bratu-type equation

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...

solving nonlinear klein-gordon equation with a quadratic nonlinear term using homotopy analysis method

in this paper, nonlinear klein-gordon equation with quadratic term is solved by means of an analytic technique, namely the homotopy analysis method (ham).comparisons are made between the adomian decomposition method (adm), the exact solution and homotopy analysis method. the results reveal that the proposed method is very effective and simple.