In this paper, we present homotopy perturbation method (HPM) for solving the Korteweg-de Vries (KdV) equation and convergence study of homotopy perturbation method for nonlinear partial differential equation. We compared our solution with the exact solution and homotopy analysis method (HAM). The results show that the HPM is an appropriate method for solving nonlinear equation.

in this work, we conduct a comparative study among the combine laplace transform and modied adomian decomposition method (lmadm) and two traditional methods for an analytic and approximate treatment of special type of nonlinear volterra integro-differential equations of the second kind. the nonlinear part of integro-differential is approximated by adomian polynomials, and the equation is red...

In this paper, the solution of the evolutionaryfourth-order in space, Sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{HPM}). The results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

In chemical engineering, several processes are represented by singular boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTM-Pad´e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for sol...

the present research attempts to explain dynamic pull-in instability of functionally graded micro-cantilevers actuated by step dc voltage while the fringing-field effect is taken into account in the vibrational equation of motion. by employing modern asymptotic approach namely homotopy perturbation method with an auxiliary term, high-order frequency-amplitude relation is obtained, then the infl...

We apply the homotopy perturbation method for solving the fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of ...