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Madani, Mohammad; Fathizadeh, Mahdi; Khan, Yasir; Yildirim, Ahmet

On the coupling of the homotopy perturbation method and Laplace transformation. (English) Zbl 1219.65121

Math. Comput. Modelling 53, No. 9-10, 1937-1945 (2011).
Summary: 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.

Cited in 47 Documents

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
44A10 Laplace transform

Keywords:

Laplace homotopy perturbation method (LHPM); homotopy perturbation method (HPM); non-homogeneous partial differential equation
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\textit{M. Madani} et al., Math. Comput. Modelling 53, No. 9--10, 1937--1945 (2011; Zbl 1219.65121)
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