The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

In the research, nonlinear volterra partial integro-differential equation is considered. This paper compares the Homotopy Perturbation Method (HPM) with Variational Iteration Method (VIM) for solving this equation. Compared with the Adomian Decomposition Method (ADM), the methods used for this equation need less work. The results of applying these methods show the simplicity and efficiency of t...

The nonlinear two-dimensional forced-convection boundary-layer magneto hydrodynamic MHD incompressible flow of nanofluid over a horizontal stretching flat plate with variable magnetic field including the viscous dissipation effect is solved using the homotopy perturbation method HPM . In the present work, our results of the HPM are compared with the results of simulation using the finite differ...

In this paper, the problem of forced convection over a horizontal flat plate under condition of variable plate temperature is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This paper provides good supplements to the existing literature and generalizes the previ...

Abstract: The traditional perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear and linear problems. To overcome address this shortcoming, two new powerful recent analytical methods are introduced to solve heat transfer problems in this work. One is He's variational iteration method (VIM) and the other is He’s homotopy-perturbation method (HPM)....

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

This paper presents the application of the Homotopy Analysis Method (HAM) as a numerical solution to linear integro-differential equation. The HAM contains the auxiliary parameter , taht provides a powerful tool to analyze strongly linear and nonlinear problems. Examples are provided to demonstrate the advantages of HAM over the homotopy perturbation method (HPM), sine-cosine wavelets and CAS w...

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we ...

Nonlinear differential equations arise in a wide variety of problems such as fluid dynamics, quantum field theory, and plasma physics to describe the various phenomena. These problems, a limited number of them apart, do not have a precise analytical solution, so these nonlinear equations should be solved using approximate methods. The homotopy perturbation method (HPM), first proposed by He in ...

In the present paper, The homotopy perturbation method (HPM) is applied to obtain approximate analytical solutions of the fractional non-linear Schrodinger equations. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. Finally, we have illustrated the ability of the method for solving fractional non linear equation by some examples.