Stochastic Numerical Models of Oscillatory Phenomena

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.

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