Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems
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2018
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Authors
N. R. Anakira
- Department of Mathematics, Faculty of Science and Technology, Irbid National University, 2600 Irbid, Jordan.
A. k. Alomari
- Department of Mathematics, Faculty of Science, Yarmouk University, 211-63 Irbid, Jordan.
A. F. Jameel
- School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Kedah, Sintok, 06010, Malaysia.
I. Hashim
- School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia.
Abstract
In this paper, a new approximate analytical algorithm namely multistage optimal homotopy asymptotic
method (MOHAM) is presented for the first time to obtain approximate analytical solutions for linear,
nonlinear and system of initial value problems (IVPs). This algorithm depends on the standard optimal
homotopy asymptotic method (OHAM), in which it is treated as an algorithm in a sequence of subinterval.
The main advantage of this study is to obtain continuous approximate analytical solutions for a long time
span. Numerical examples are tested to highlight the important features of the new algorithm. Comparison
of the MOHAM results, standard OHAM, available exact solution and the fourth-order Runge Kutta (RK4)
reveale that this algorithm is effective, simple and more impressive than the standard OHAM for solving
IVPs.
Share and Cite
ISRP Style
N. R. Anakira, A. k. Alomari, A. F. Jameel, I. Hashim, Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 4, 1826--1843
AMA Style
Anakira N. R., Alomari A. k., Jameel A. F., Hashim I., Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems. J. Nonlinear Sci. Appl. (2016); 9(4):1826--1843
Chicago/Turabian Style
Anakira, N. R., Alomari, A. k., Jameel, A. F., Hashim, I.. "Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems." Journal of Nonlinear Sciences and Applications, 9, no. 4 (2016): 1826--1843
Keywords
- Optimal homotopy asymptotic method (OHAM)
- multistage optimal homotopy asymptotic method (MOHAM)
- initial value problems
- series solution
- Mathematica 9.
MSC
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