Comparison between homotopy analysis method and optimal homotopy asymptotic method for nth‐order integro‐differential equation |
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Authors: | M. Ghoreishi A. I. B. MD. Ismail A. K. Alomari |
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Affiliation: | 1. School of Mathematical Science, Universiti Sains Malaysia, , 11800 Penang, Malaysia;2. Department of Sciences, Faculty of Science, Jerash University, , 26150 Jerash, Jordan |
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Abstract: | This paper presents general framework for solving the nth‐order integro‐differential equation using homotopy analysis method (HAM) and optimal homotopy asymptotic method (OHAM). OHAM is parameter free and can provide better accuracy over the HAM at the same order of approximation. Furthermore, in OHAM the convergence region can be easily adjusted and controlled. Comparison, via two examples, between our solution using HAM and OHAM and the exact solution shows that the HAM and the OHAM are effective and accurate in solving the nth‐order integro‐differential equation. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | nth‐order integro‐differential equation homotopy analysis method optimal homotopy asymptotic method series solution |
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