A new technique of using homotopy analysis method for solving high‐order nonlinear differential equations |
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| Authors: | Hany N Hassan Magdy A El‐Tawil |
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| Institution: | 1. Department of Basic Science, High Institute of Technology, Benha University, Benha 13512, Egypt;2. Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza Egypt |
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| Abstract: | In this paper, a new technique of homotopy analysis method (HAM) is proposed for solving high‐order nonlinear initial value problems. This method improves the convergence of the series solution, eliminates the unneeded terms and reduces time consuming in the standard homotopy analysis method (HAM) by transform the nth‐order nonlinear differential equation to a system of n first‐order equations. Second‐ and third‐ order problems are solved as illustration examples of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. |
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| Keywords: | nonlinear initial value problems homotopy analysis method modified HAM system of differential equations |
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