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Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method
Pure and Applied Mathematics Journal
Volume 4, Issue 5, October 2015, Pages: 219-224
Received: Jun. 8, 2015; Accepted: Jun. 15, 2015; Published: Sep. 8, 2015
Author
Khalid Suliman Aboodh, Department of Mathematics, Faculty of Science & technology, Omdurman Islamic University, Khartoum, Sudan
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Abstract
Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.
Keywords
Aboodh Transform, Homotopy Perturbation Method, Linear Partial Differential Equation
Khalid Suliman Aboodh, Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method, Pure and Applied Mathematics Journal. Vol. 4, No. 5, 2015, pp. 219-224. doi: 10.11648/j.pamj.20150405.13
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