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Journal of Mathematical Chemistry

, Volume 56, Issue 10, pp 2876–2897 | Cite as

Adapted numerical modelling of the Belousov–Zhabotinsky reaction

  • Raffaele D’Ambrosio
  • Martina Moccaldi
  • Beatrice Paternoster
  • Federico Rossi
Original Paper
  • 102 Downloads

Abstract

Adapted numerical schemes for the integration of differential equations generating periodic wavefronts have reported benefits in terms of accuracy and stability. This work is focused on differential equations modelling chemical phenomena which are characterized by an oscillatory dynamics. The adaptation is carried out through the exponential fitting technique, which is specially suitable to follow the apriori known qualitative behavior of the solution. In particular, we have merged this strategy with the information coming from existing theoretical studies and especially the observation of time series. Numerical tests will be provided to show the effectiveness of this problem-oriented approach.

Keywords

Oscillating solutions Exponential fitting Adapted Runge–Kutta methods Parameter estimation Reaction equations Belousov–Zhabotinsky reaction Chemical oscillators 

Notes

Acknowledgements

Raffaele D’Ambrosio, Martina Moccaldi and Beatrice Paternoster are members of the INdAM Research group GNCS. The work is supported by GNCS-Indam project.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Raffaele D’Ambrosio
    • 1
  • Martina Moccaldi
    • 2
  • Beatrice Paternoster
    • 2
  • Federico Rossi
    • 3
  1. 1.Department of Engineering and Computer Science and MathematicsUniversity of L’AquilaL’AquilaItaly
  2. 2.Department of MathematicsUniversity of SalernoFiscianoItaly
  3. 3.Department of Chemistry and BiologyUniversity of SalernoFiscianoItaly

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