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Comparison between homotopy analysis method and optimal homotopy asymptotic method for n th‐order integro‐differential equation
Author(s) -
Ghoreishi M.,
Ismail A. I. B. MD.,
Alomari A. K.
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1483
Subject(s) - mathematics , homotopy analysis method , homotopy , homotopy perturbation method , differential equation , convergence (economics) , order (exchange) , mathematical analysis , pure mathematics , finance , economics , economic growth
This paper presents general framework for solving the n th‐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 n th‐order integro‐differential equation. Copyright © 2011 John Wiley & Sons, Ltd.