Application of New Homotopy Perturbation Method for Solving Partial Differential Equations

Abstract

In this paper, a novel technique, that is to read, the New Homotopy Perturbation Method (NHPM) is utilized for solving a linear and non-linear differential equations and integral equations. The two most important steps in the application of the new homotopy perturbation method are to invent a suitable homotopy equation and to choose a suitable initial conditions. Comparing between the effects of the method (NHPM), is given exact solution, and the method (HPM), is given approximate solution, in this paper, we make some instances are provided to prove the ability of the method (NHPM). Show that the method (NHPM) is valid and effective, easy and accurate in solving linear and nonlinear differential equations, compared with the Homotopy Perturbation Method (HPM).

Solving time-fractional Navier–Stokes equations using homotopy perturbation Elzaki transform

“…It is also demonstrated that the results obtained from the present method are in excellent agreement with the results by other methods. It is shown that the proposed method is found to be reliable, efficient and easy to implement for various related problems of science and engineering.non-linear partial differential equations are also solved by different authors [22,23] using modified HPM. The primary equation of movement of viscous fluid flow known as the NS equation has been presented in 1822 [24].…”

“…non-linear partial differential equations are also solved by different authors [22,23] using modified HPM. The primary equation of movement of viscous fluid flow known as the NS equation has been presented in 1822 [24].…”

Homotopy perturbations method: Theoretical as­pects and applications

“…After that, the extensive development and application of this method to various fields of science researches has been started. For instance, the HPM has been successfully applied for obtaining analytic or approximate solutions of nonlinear differential and partial-differential equations (Biazar et al, 2009;El-Sayed et al, 2012;Gadallah & Elzaki, 2017), as well as Fredholm and Volterra integral equations (Hetmaniok et al, 2012(Hetmaniok et al, , 2013Dong et al, 2013). Furthermore, this method also has found significant application in solving many kinds of real based problems, mainly in the physical sciences (Zeb et al, 2014;Kevkić et al, 2017Kevkić et al, , 2018.…”