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 known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) 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 reduce 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.
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September 2017
Research-Article
An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty
Ali Ahmadian,
Ali Ahmadian
Department of Mathematics,
Faculty of Science,
University Putra Malaysia,
Serdang 43400 UPM, Selangor, Malaysia
e-mail: ahmadian.hosseini@gmail.com
Faculty of Science,
University Putra Malaysia,
Serdang 43400 UPM, Selangor, Malaysia
e-mail: ahmadian.hosseini@gmail.com
Search for other works by this author on:
Soheil Salahshour,
Soheil Salahshour
Young Researchers and Elite Club,
Mobarakeh Branch,
Islamic Azad University,
Mobarakeh 19166, Iran
e-mail: soheilsalahshour@yahoo.com
Mobarakeh Branch,
Islamic Azad University,
Mobarakeh 19166, Iran
e-mail: soheilsalahshour@yahoo.com
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Chee Seng Chan,
Chee Seng Chan
Centre of Image and Signal Processing,
Faculty of Computer Science and
Information Technology,
University of Malaya,
Kuala Lumpur 50603, Malaysia
e-mail: cs.chan@um.edu.my
Faculty of Computer Science and
Information Technology,
University of Malaya,
Kuala Lumpur 50603, Malaysia
e-mail: cs.chan@um.edu.my
Search for other works by this author on:
Dumitur Baleanu
Dumitur Baleanu
Department of Mathematics and
Computer Science,
Cankaya University,
Balgat 06530, Ankara, Turkey;
Computer Science,
Cankaya University,
Balgat 06530, Ankara, Turkey;
Search for other works by this author on:
Ali Ahmadian
Department of Mathematics,
Faculty of Science,
University Putra Malaysia,
Serdang 43400 UPM, Selangor, Malaysia
e-mail: ahmadian.hosseini@gmail.com
Faculty of Science,
University Putra Malaysia,
Serdang 43400 UPM, Selangor, Malaysia
e-mail: ahmadian.hosseini@gmail.com
Soheil Salahshour
Young Researchers and Elite Club,
Mobarakeh Branch,
Islamic Azad University,
Mobarakeh 19166, Iran
e-mail: soheilsalahshour@yahoo.com
Mobarakeh Branch,
Islamic Azad University,
Mobarakeh 19166, Iran
e-mail: soheilsalahshour@yahoo.com
Chee Seng Chan
Centre of Image and Signal Processing,
Faculty of Computer Science and
Information Technology,
University of Malaya,
Kuala Lumpur 50603, Malaysia
e-mail: cs.chan@um.edu.my
Faculty of Computer Science and
Information Technology,
University of Malaya,
Kuala Lumpur 50603, Malaysia
e-mail: cs.chan@um.edu.my
Dumitur Baleanu
Department of Mathematics and
Computer Science,
Cankaya University,
Balgat 06530, Ankara, Turkey;
Computer Science,
Cankaya University,
Balgat 06530, Ankara, Turkey;
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 9, 2016; final manuscript received March 27, 2017; published online May 4, 2017. Assoc. Editor: Corina Sandu.
J. Comput. Nonlinear Dynam. Sep 2017, 12(5): 051008 (13 pages)
Published Online: May 4, 2017
Article history
Received:
April 9, 2016
Revised:
March 27, 2017
Citation
Ahmadian, A., Salahshour, S., Chan, C. S., and Baleanu, D. (May 4, 2017). "An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty." ASME. J. Comput. Nonlinear Dynam. September 2017; 12(5): 051008. https://doi.org/10.1115/1.4036419
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