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Math. Comput. Appl. 2010, 15(3), 481-489; doi:10.3390/mca15030481

Analytical Aspect of Fourth-Order Parabolic Partial Differential Equations with Variable Coefficients

1
Department of Mathematics, University of Karachi, Karachi-75270, Pakistan
2
Department of Mathematics & Basic Sciences, NEDUET, Karachi-75270, Pakistan
*
Author to whom correspondence should be addressed.
Published: 1 December 2010
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Abstract

In this work, the homotopy analysis method (HAM) is applied to solve the fourth-order parabolic partial differential equations. This equation practically arises in the transverse vibration problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Some applications are given to verify the reliability and efficiency of the method. The convergence control parameter h in the HAM solutions has provided a convenient way of controlling the convergence region of series solutions. It is also shown that the solutions that are obtained by Adomian decomposition method (ADM) and variational iteration method (VIM) are special cases of the solutions obtained by HAM.
Keywords: Fourth-order parabolic partial differential equations; Homotopy analysis method; Convergence control parameter; transverse vibrations Fourth-order parabolic partial differential equations; Homotopy analysis method; Convergence control parameter; transverse vibrations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Khan, N.A.; Ara, A.; Afzal, M.; Khan, A. Analytical Aspect of Fourth-Order Parabolic Partial Differential Equations with Variable Coefficients. Math. Comput. Appl. 2010, 15, 481-489.

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