Title: Solving first-order fuzzy initial value problems using one-step scheme with second and third fuzzy derivatives

Authors: Kashif Hussain; Oluwaseun Adeyeye; Nazihah Ahmad

Addresses: School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Sintok, 06010, Malaysia ' School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Sintok, 06010, Malaysia ' School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Sintok, 06010, Malaysia

Abstract: Fuzzy differential equations model the uncertain behaviour of the dynamic model. In cases where the exact solution does not exist, numerical methods are adopted to obtain an approximate solution of these equations. Although there are several numerical approaches in the literature, the accuracy of the existing numerical methods for solving linear and non-linear first-order fuzzy initial value problems (FIVPs) in terms of absolute error could be improved. For this reason, this paper develops a one-step implicit method with the presence of higher fuzzy derivatives to obtain the numerical solution of both linear and non-linear first-order FIVPs. First, the convergence properties of the one-step method are described in detail using the definition of zero-stability and consistency for linear multistep methods. Then the one-step scheme with second and third fuzzy derivatives is adopted to solve some first-order FIVPs. The results indicate that the proposed method efficiently solves fuzzy initial value problems.

Keywords: fuzzy set theory; fuzzy derivatives; FIVPs; fuzzy initial value problems; first-order; one-step; implicit method.

DOI: 10.1504/IJCSM.2023.133529

International Journal of Computing Science and Mathematics, 2023 Vol.18 No.1, pp.80 - 93

Received: 05 Jul 2021
Accepted: 07 Feb 2022
Published online: 19 Sep 2023 *

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