Homotopy perturbation method HPM and boundary element method BEM for calculating the exact and numerical solutions of Poisson equation with appropriate boundary and initial conditions are presented. Exact solutions of electrostatic potential problems defined by Poisson equation are found using HPM given boundary and initial conditions. The same problems are also solved using the BEM. The cell i...

To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of linear and nonlinear parabolic hyperbolic partial differential equations (PDEs) subject initial boundary conditions integral type, the homotopy perturbation method (HPM) is utilized in this study. The HPM used solve specified IBVPs, which are then transformed into local Dirichlet IBVPs. Some examples de...

In this paper, a Laplace transform decomposition algorithm (LTDA) is proposed to solve the Riccati equation. Comparisons are made among the homotopy perturbation method (HPM), the Adomian decomposition method (ADM) and the proposed method. It is shown that the homotopy perturbation method with a specific convex homotopy is equivalent to the Adomian decomposition method and the Laplace transform...

In this paper , we have presented Homotopy Perturbation Method (HPM) to solve nonlinear parabolic equation with nonlocal boundary conditions. This method provides an analytical solution by utilizing only the initial condition. The HPM allows for the solution of the nonlinear parabolic equations to be calculated in the form of a series with easily computable components. The obtained results are ...

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differ...

In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the pro...

The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbat...

In this work, a powerful analytical method called homotopy perturbation method (HPM) is used to obtain the series solution for nonlinear problems in classic dynamics. The governing equations are obtained using the Lagrange method and solved analytically by HPM. The present solution gives an expression which is valid for the whole domain of the solution. Comparisons of the obtained solutions wit...

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.

Nonlinear problems are more challenging and almost complex to be solved. A recently developed Homotopy Perturbation Method (HPM) is introduced. This method is used to represent the system as a less complicated (almost linear) model. To verify the effectiveness, HPM based model is compared with the nonlinear dynamic in both open and closed loop PI controlled. The error indices are approximation ...