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Title: New semi-analytical method for solving two point nth order fuzzy boundary value problem

Authors: A.F. Jameel; N.R. Anakira; A.K. Alomari; D.M. Alsharo; A. Saaban

Addresses: School of Quantitative Sciences, College Of Art and Sciences, Universiti Utara Malaysia (UUM), Sintok, 06010 Kedah, Malaysia ' Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, 2600, Jordan ' Faculty of Science, Department of Mathematics, Yarmouk University, Irbid 211-63, Jordan ' Applied Science Department, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan ' School of Quantitative Sciences, College Of Art and Sciences, Universiti Utara Malaysia (UUM), Sintok, 06010 Kedah, Malaysia

Abstract: In this paper, a semi analytical algorithm, namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an infinite series with the components that can be easily calculated. The HAM utilises a convergence control parameter to control the convergence region of the infinite series solution. Numerical experiment is tested to highlight the important features of the HAM algorithm. Comparison of the HAM results and available exact solution reveal that this algorithm is effective and simple and for solving TPFBVP.

Keywords: fuzzy numbers; two point fuzzy boundary value problems; HAM; homotopy analysis method.

DOI: 10.1504/IJMMNO.2019.096906

International Journal of Mathematical Modelling and Numerical Optimisation, 2019 Vol.9 No.1, pp.12 - 31

Received: 07 Jan 2017
Accepted: 18 Nov 2017

Published online: 11 Dec 2018 *

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