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Journal of Porous Media
IF: 1.49 5-Year IF: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v11.i8.50
pages 765-778

Use of He's Homotopy Perturbation Method for Solving a Partial Differential Equation Arising in Modeling of Flow in Porous Media

Mehdi Dehghan
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15914, Iran
Fatemeh Shakeri
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15914, Iran

ABSTRACT

The Boussinesq-type equations serve as models in many branches of science and engineering. Recently, much attention has been expended in studying these equations, and there has been a considerable mathematical interest in them. In this work, we present the solution of a generalized Boussinesq equation by means of the homotopy perturbation method. The homotopy perturbation method is an analytical procedure for finding the solutions of differential equations that is based on constructing a homotopy with an imbedding parameter p ∈ [0,1], which is considered to be a so-called small parameter. Application of the homotopy perturbation technique to this problem shows the rapid convergence of this method to the exact solution. The approximations obtained by the proposed method are uniformly valid not only for small parameters, but also for very large parameters. Moreover, this technique does not require any discretization, linearization, or small perturbations and therefore reduces the numerical computations by a great deal.


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