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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with Association for Scientific Research (ASR).
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Article

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

by
Najeeb Alam Khan
1,
Asmat Ara
1,
Muhammad Afzal
1 and
Azam Khan
2,*
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.
Math. Comput. Appl. 2010, 15(3), 481-489; https://doi.org/10.3390/mca15030481
Published: 1 December 2010
Versions Notes

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

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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. https://doi.org/10.3390/mca15030481

AMA Style

Khan NA, Ara A, Afzal M, Khan A. Analytical Aspect of Fourth-Order Parabolic Partial Differential Equations with Variable Coefficients. Mathematical and Computational Applications. 2010; 15(3):481-489. https://doi.org/10.3390/mca15030481

Chicago/Turabian Style

Khan, Najeeb Alam, Asmat Ara, Muhammad Afzal, and Azam Khan. 2010. "Analytical Aspect of Fourth-Order Parabolic Partial Differential Equations with Variable Coefficients" Mathematical and Computational Applications 15, no. 3: 481-489. https://doi.org/10.3390/mca15030481

APA Style

Khan, N. A., Ara, A., Afzal, M., & Khan, A. (2010). Analytical Aspect of Fourth-Order Parabolic Partial Differential Equations with Variable Coefficients. Mathematical and Computational Applications, 15(3), 481-489. https://doi.org/10.3390/mca15030481

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