Multistage Optimal Homotopy Asymptotic Method for Solving Initial-Value Problems


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.


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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


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