On the coupling of the homotopy perturbation method and Laplace transformation

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• 作者：Mohammad Madani^a ; Mahdi Fathizadeh^a ; Yasir Khan^b ; ^{yasirmath@yahoo.com} ; Ahmet Yildirim^c
• 关键词：Laplace Homotopy Perturbation Method (LHPM) ; Homotopy Perturbation Method (HPM) ; Non-homogeneous partial differential equation
• 刊名：Mathematical and Computer Modelling
• 出版年：2011
• 出版时间：May 2011
• 年：2011
• 卷：53
• 期：9-10
• 页码：1937-1945
• 全文大小：558 K

文摘

In this paper, a Laplace homotopy perturbation method is employed for solving one-dimensional non-homogeneous partial differential equations with a variable coefficient. This method is a combination of the Laplace transform and the Homotopy Perturbation Method (LHPM). LHPM presents an accurate methodology to solve non-homogeneous partial differential equations with a variable coefficient. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as HPM, VIM, and ADM. The approximate solutions obtained by means of LHPM in a wide range of the problem’s domain were compared with those results obtained from the actual solutions, the Homotopy Perturbation Method (HPM) and the finite element method. The comparison shows a precise agreement between the results, and introduces this new method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.