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Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method

Atangana, Abdon and Kilicman, Adem (2013) Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method. Abstract and Applied Analysis, 2013 . art. no. 380484. pp. 1-9. ISSN 1085-3375; ESSN: 1687-0409

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Abstract

The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as N tends to infinity.

Item Type:Article
Keyword:Boundary value problems; Poisson equations; Biharmonic equations; Numerical solution
Faculty or Institute:Faculty of Science
Institute for Mathematical Research
Publisher:Hindawi Publishing Corporation
DOI Number:10.1155/2013/380484
Altmetrics:http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/380484
ID Code:30188
Deposited By: Umikalthom Abdullah
Deposited On:25 Aug 2014 14:57
Last Modified:31 Mar 2016 16:24

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