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Stochastic Numerical Models of Oscillatory Phenomena

  • Raffaele D’Ambrosio
  • Martina Moccaldi
  • Beatrice Paternoster
  • Federico Rossi
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 830)

Abstract

The use of time series for integrating ordinary differential equations to model oscillatory chemical phenomena has shown benefits in terms of accuracy and stability. In this work, we suggest to adapt also the model in order to improve the matching of the numerical solution with the time series of experimental data. The resulting model is a system of stochastic differential equations. The stochastic nature depends on physical considerations and the noise relies on an arbitrary function which is empirically chosen. The integration is carried out through stochastic methods which integrate the deterministic part by using one-step methods and approximate the stochastic term by employing Monte Carlo simulations. Some numerical experiments will be provided to show the effectiveness of this approach.

Keywords

Oscillating solutions Belousov-Zhabotinsky reaction Reaction equations Stochastic chemical oscillators Stochastic models Stochastic differential equations 

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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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