Homotopy Perturbation Method with the help of Adomian decomposition method for nonlinear problems

Mathematical Analysis and its Contemporary Applications

دوره 4، شماره 1، فروردین 2022، صفحه 45-51   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/maca.2021.1944809.1038

نویسنده

Soumeyeh Khaleghizadeh^*

Departmant of Mathematics,Payame Noor University,Tehran,Iran

چکیده

This paper concerns He's Homotopy Perturbation Method (HPM) which has been applied to solve some nonlinear differential equations. In HPM, at first, we construct a homotopy that satisfies an equation which is called the perturbation equation. Moreover, in this method, the solution is considered as power series in $p$. By substituting this series into an equation and equating the coefficient of the terms with identical powers of $p$, the researcher obtained a set of equations. These equations can be solved in various methods. Here Adomian decomposition method (ADM) is employed for solving equations, obtained from the homotopy perturbation method.

کلیدواژه‌ها

Homotopy perturbation method؛ Nonlinear؛ Adomian decomposition method