Guaranteed predictive estimation of solutions of system of differential equations with the Gompertzian dynamics

2019;
: pp. 92-100
https://doi.org/10.23939/mmc2019.01.092
Received: March 20, 2019
Accepted: May 02, 2019
1
Taras Shevchenko National University of Kyiv
2
Taras Shevchenko National University of Kyiv
3
Taras Shevchenko National University of Kyiv

In this paper, we have introduced a mathematical model to describe processes that grow in time rapidly.  The model has the form of a system of non-linear differential equations with Gompertzian dynamics and non-stationary parameters.  We have formulated and studied the  problem of finding the predictive estimation for the systems of differential equations with Gompertzian dynamics, for the case of continuous observation.  We have suggested the algorithms for building guaranteed predictive estimations for the model.  We have presented as an example, the results of numerical experiments to build guaranteed estimates for the mathematical model of spreading some type of information in society.  The suggested approach presents both theoretical interest and important practical meaning.

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Math. Model. Comput. Vol.6, No.1, pp.92-100 (2019)