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An Interval Insight to Adomian Decomposition Method for Ordinary Differential Systems by Considering Uncertain Coefficients with Chebyshev Polynomials

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Proceedings of the 5th Brazilian Technology Symposium (BTSym 2019)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 201))

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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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Author information

Authors and Affiliations

  1. Department of Electrical and Control Engineering, Tafresh University, Tafresh, 39518 79611, Iran

    Navid Razmjooy & Mehdi Ramezani

  2. Department of Telecommunications, Fluminense Federal University (UFF), Niteroi, RJ, Brazil

    Vania V. Estrela

Authors
  1. Navid Razmjooy
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  2. Mehdi Ramezani
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  3. Vania V. Estrela
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Corresponding author

Correspondence to Navid Razmjooy .

Editor information

Editors and Affiliations

  1. School of Electrical and Computer Engineering (FEEC), UNICAMP, Campinas, São Paulo, Brazil

    Yuzo Iano

  2. School of Technology (FT), UNICAMP, Limeira, São Paulo, Brazil

    Rangel Arthur

  3. Divisão de Engenharia Eletrônica, Instituto Tecnológico de Aeronáutica, São José dos Campos, São Paulo, Brazil

    Osamu Saotome

  4. Universidad Peruana de Ciencias Aplicada, Lima, Peru

    Guillermo Kemper

  5. School of Electrical and Computer Engineering (FEEC), UNICAMP, Campinas, São Paulo, Brazil

    Reinaldo Padilha França

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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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  • DOI: https://doi.org/10.1007/978-3-030-57548-9_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57547-2

  • Online ISBN: 978-3-030-57548-9

  • eBook Packages: EngineeringEngineering (R0)

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