This method is based on a combination of the homotopy perturbation method (HPM) and the reproducing kernel method (RKM). The main advantages of this method is that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of homotopy perturbation method. The solution obtained using the method takes the form of a convergent series ...

Although homotopy-based methods, namely homotopy analysis method and homotopy perturbation method, have largely been used to solve functional equations, there are still serious questions on the convergence issue of these methods. Some authors have tried to prove convergence of these methods, but the researchers in this article indicate that some of those discussions are faulty. Here, after crit...

In this paper, we propose a combined form of the sumudu transform method with the homotopy perturbation method to solve nonlinear equations. This method is called the homotopy perturbation sumudu transform method (HPSTM). The nonlinear terms can be easily handled by the use of He’s polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoi...

in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...

in this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order sawada-kotera (ssk) and a lax'sseven-order kdv (lskdv) equations. then obtain the exact solitary-wave so-lutions and numerical solutions of the ssk and lskdv equations for the initialconditions. the numerical solutions are compared with the known analyticalsolutions. their rem...

In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.

In this paper, we apply the homotopy perturbation transform method (HPTM) to obtain the solution of linear and nonlinear Schrödinger equations. The HPTM is a combined form of the Laplace transform method with the homotopy perturbation method. This method finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that this technique solves ...

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations. This method is called the homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He’s polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the...

The aim of this paper is to find the exact solution of nonlinear integro-differential equations using a novel enhanced mo dified homotopy perturbation method. To achieve this goal, we apply the new modified technique and enhance it by separating the known analytic function into two parts. Several examples are provided to present the strength and rapid convergence of proposed method. Some of the...