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 this article Optimal Homotopy Asymptotic Method (OHAM) is used for the solution of homogenous advection equations. The accuracy of the method is analyzed by its comparison with exact and Homotopy Perturbation transforms Method (HPTM) solution. The absolute errors and order of approximation presented.

Some recently developed analytical methods namely; homotopy analysis method, homotopy perturbation method and modified homotopy perturbation method are applied successfully for solving strongly nonlinear oscillators. The analytical results obtained by using HAM are compared with those of HPM, mHPM as well as with numerical results. In this study, different examples with strong nonlinearity are ...

Recently, Wazwaz has studied the regularization method to one-dimensional linear Fredholm integral equations of first kind [Wazwaz, 2011]. In this work, we develop for and nonlinear two-dimensional Fred-holm kind. Indeed, is used directly. But are transformed linearintegral by a change variable; then, The Regularization-Homotopy Method applied. combination homotopy perturbation method, or short...

in this paper, the magnetohydrodynamic (mhd) boundary layer flow over a nonlinear porous stretching sheet is investigated by employing the homotopy perturbation transform method (hptm) and the pade´ approximation. the numerical solution of the governing non-linear problem is developed. comparison of the present solution is made with the existing solution and excellent agreement is noted. graphi...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems.

Infectious diseases like measles, tuberculosis, cholera, diarrhea, COVID-19, and staphylococcal infection continue to receive a lot of attention daily due their high rate transmission deadly nature. Thus, in this study, the analytical solution dynamics diarrhea was studied using Homotopy perturbation approach. The human population divided into five major compartments namely: susceptible, infect...

We show that the Adomian decomposition method, the time–series expansion, the homotopy–perturbation method, and the variational– iteration method completely fail to provide a reasonable description of the dynamics of the simplest prey–predator system. In is well known that a reasonable description of the dynamics of a nonlinear system by means of a perturbation method is a difficult enterprize ...

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...