A Novel Iterative Numerical Algorithm for the Solutions of Systems of Fuzzy Initial Value Problems

Authors

Omar Abu Arqub, Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanFollow
Shaher Momani, Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan\\ \Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University (KAU), Jeddah 21589, Saudi ArabiaFollow
Saleh Al-Mezel, Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University (KAU), Jeddah 21589, Saudi ArabiaFollow
Marwan Kutbi, Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University (KAU), Jeddah 21589, Saudi ArabiaFollow

Author Country (or Countries)

Saudi Arabia

Abstract

Behaviors of many dynamic systems with uncertainty can be modelled effectively by systems of fuzzy differential equations. In this paper, we develop new numerical iterative method for solving systems of fuzzy initial value problems based on the reproducing kernel theory under the assumption of Hukuhara differentiability. The exact and approximate solutions are given with series form in terms of their parametric form, where two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values. Furthermore, error estimation is proved in order to capture the behavior of fuzzy solutions. Applicability, potentiality, and efficiency of the proposed algorithm for the fuzzy solutions of different fuzzy systems are investigated using computer tables and graphical representation.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110412

Recommended Citation

Abu Arqub, Omar; Momani, Shaher; Al-Mezel, Saleh; and Kutbi, Marwan (2017) "A Novel Iterative Numerical Algorithm for the Solutions of Systems of Fuzzy Initial Value Problems," Applied Mathematics & Information Sciences: Vol. 11: Iss. 4, Article 12.
DOI: http://dx.doi.org/10.18576/amis/110412
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss4/12