Abstract
Generally, parameters in the mathematical models of engineering problems are considered deterministic, although, in practice, there are always some uncertainties in the model parameters. Uncertainty can make an accurate or even wrong representation for the analyzed model. There is a wide reason which causes the uncertainties, like measurement error, inhomogeneity of the process, etc. This problem leads researches to analyze the problem from a different point of view. When the uncertainty is present in the process, traditional methods of exact values cannot solve the problem with no inaccuracies and mistakes. Interval analysis is a method that can be utilized to solve these kinds of problems. In this paper, an interval Adomian decomposition method combined with Chebyshev polynomial is introduced. The proposed interval Adomian method is then validated through ODE systems. The simulation results are applied on four practical case studies, and the results are compared with interval Euler and Taylor methods. The final results show that the proposed methodology has good accuracy to find the proper interval and to effectively handle the wrapping effect to sharpen the range of non-monotonic intervals.
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Razmjooy, N., Ramezani, M., Estrela, V.V. (2021). An Interval Insight to Adomian Decomposition Method for Ordinary Differential Systems by Considering Uncertain Coefficients with Chebyshev Polynomials. In: Iano, Y., Arthur, R., Saotome, O., Kemper, G., Padilha França, R. (eds) Proceedings of the 5th Brazilian Technology Symposium. BTSym 2019. Smart Innovation, Systems and Technologies, vol 201. Springer, Cham. https://doi.org/10.1007/978-3-030-57548-9_23
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