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http://dx.doi.org/10.14317/jami.2013.165

ANALYTICAL SOLUTION OF SINGULAR FOURTH ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS OF VARIABLE COEFFICIENTS BY USING HOMOTOPY PERTURBATION TRANSFORM METHOD  

Gupta, V.G. (Department of Mathematics, University of Rajasthan)
Gupta, Sumit (Department of Mathematics, Jagan Nath Gupta Institute of Engineering and Technology)
Publication Information
Journal of applied mathematics & informatics / v.31, no.1_2, 2013 , pp. 165-177 More about this Journal
Abstract
In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. 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 Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this 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.
Keywords
Homotopy perturbation method; Laplace Transform Method; Fourth-order parabolic equations; He's Polynomials; Analytical Solution;
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