Mathematics and Statistics Vol. 8(5), pp. 527 - 534
DOI: 10.13189/ms.2020.080505
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Comparison for the Approximate Solution of the Second-Order Fuzzy Nonlinear Differential Equation with Fuzzy Initial Conditions

Ali F Jameel ^1,*, Akram H. Shather ², N.R. Anakira ³, A. K. Alomari ⁴, Azizan Saaban ^1
1 School of Quantitative Sciences, College of Art and Sciences, Universiti Utara Malaysia (UUM), Malaysia
² Department of Computer Engineering Techniques, Al-Kitab University Altun Kupri, Iraq
³ Department of Mathematics, Faculty of Science and Technology, Irbid National University, Jordan
⁴ Department of Mathematics, Faculty of Science, Yarmouk University, Jordan

ABSTRACT

This research focuses on the approximate solutions of second-order fuzzy differential equations with fuzzy initial condition with two different methods depending on the properties of the fuzzy set theory. The methods in this research based on the Optimum homotopy asymptotic method (OHAM) and homotopy analysis method (HAM) are used implemented and analyzed to obtain the approximate solution of second-order nonlinear fuzzy differential equation. The concept of topology homotopy is used in both methods to produce a convergent series solution for the propped problem. Nevertheless, in contrast to other destructive approaches, these methods do not rely upon tiny or large parameters. This way we can easily monitor the convergence of approximation series. Furthermore, these techniques do not require any discretization and linearization relative with numerical methods and thus decrease calculations more that can solve high order problems without reducing it into a first-order system of equations. The obtained results of the proposed problem are presented, followed by a comparative study of the two implemented methods. The use of the methods investigated and the validity and applicability of the methods in the fuzzy domain are illustrated by a numerical example. Finally, the convergence and accuracy of the proposed methods of the provided example are presented through the error estimates between the exact solutions displayed in the form of tables and figures.

KEYWORDS
Fuzzy Set Theory, Fuzzy Differential Equations, Nonlinear Fuzzy Initial Value Problem, Optimum Homotopy Asymptotic Method (OHAM), Homotopy Analysis Method (HAM)

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ali F Jameel , Akram H. Shather , N.R. Anakira , A. K. Alomari , Azizan Saaban , "Comparison for the Approximate Solution of the Second-Order Fuzzy Nonlinear Differential Equation with Fuzzy Initial Conditions," Mathematics and Statistics, Vol. 8, No. 5, pp. 527 - 534, 2020. DOI: 10.13189/ms.2020.080505.

(b). APA Format:
Ali F Jameel , Akram H. Shather , N.R. Anakira , A. K. Alomari , Azizan Saaban (2020). Comparison for the Approximate Solution of the Second-Order Fuzzy Nonlinear Differential Equation with Fuzzy Initial Conditions. Mathematics and Statistics, 8(5), 527 - 534. DOI: 10.13189/ms.2020.080505.