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research-article

An efficient numerical simulation for solving dynamical systems with uncertainty

[+] Author and Article Information
Ali Ahmadian

Department of Mathematics Faculty of Science University Putra Malaysia 43400 UPM, Serdang, Selangor, Malaysia
ahmadian.hosseini@gmail.com

Soheil Salahshour

Young Researchers and Elite Club Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran
soheilsalahshour@yahoo.com

Chee Seng Chan

Centre of Image and Signal Processing Faculty of Computer Science & Information Technology University of Malaya 50603 Kuala Lumpur, Malaysia
cs.chan@um.edu.my

Dumitru Baleanu

Department of Mathematics and Computer Science Cankaya University 06530 Balgat, Ankara, Turkey;Institute of Space Sciences Magurele-Bucharest, R 76911, Romania
dumitru@cankaya.edu.tr

1Corresponding author.

ASME doi:10.1115/1.4036419 History: Received April 09, 2016; Revised March 27, 2017

Abstract

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well know that the usage of fuzzy differential equations (FDEs) is a natural way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge-Kutta methods is generalized that are for solving first order fuzzy dynamical systems An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduces substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

Copyright (c) 2017 by ASME
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