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.
An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty
Balgat 06530, Ankara, Turkey;
Magurele-Bucharest R 76911, Romania
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.
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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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