in this article, we demonstrate an analytic-numeric solution for some dynamical systems using the multistagehomotopy perturbation method. the method yields results that are in complete agreement with their numericalcounterparts.

Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this also to generate spherically symmetric of Einstein-scalar system Schwarzschild vacuum metric. This was then investigate effect scalar fields on bla...

In this paper, analytic solutions of two-dimensional coupled Burgers' equations are obtained by the Homotopy analysis and the Homotopy Pad$acute{e}$ methods. The obtained approximation by using Homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by $[m,m]$ Homotopy Pad$acute{e...

This investigation focuses on the impact of Stefan blowing flow hybrid nanoliquids over a moving slender needle with magnetohydrodynamics (MHD), thermal radiation, and entropy generation. To facilitate analysis, suitable transformations are applied to convert governing partial differential equations into set ordinary equations, which then solved analytically using Homotopy Analysis Method (HAM)...

The aim of present paper is to study the series solution of time dependent MHD second grade incompressible nanofluid towards a stretching sheet. The effects of mixed convection and thermal radiation are also taken into account. Because of nanofluid model, effects Brownian motion and thermophoresis are encountered. The resulting nonlinear momentum, heat and concentration equations are simplified...

In this article, the flow problem in a thin liquid film of second grade fluid over an unsteady stretching surface is investigated. By means of suitable transformations, the governing nonlinear partial differential equation has been reduced to the nonlinear ordinary differential equation. The developed nonlinear equation is solved analytically by using the homotopy analysis method (HAM). An expr...

In this paper, non-similarity boundary-layer flow of a Newtonian fluid near an asymmetric plane stagnation point with a dimensionless external flow velocity ue = x/(x + 1) is studied. The original boundary-layer equations are transferred into a nonlinear partial differential equation (PDE) with variable coefficients. An analytic technique for strongly nonlinear equations, namely the homotopy an...