Numerical Treatment of Multidimensional Stochastic, Competitive and Evolutionary Models

Mostafa Zahri ()
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Mostafa Zahri: University of Sharjah, College of Sciences

Chapter Chapter 13 in Disease Prevention and Health Promotion in Developing Countries, 2020, pp 183-215 from Springer

Abstract: Abstract In this chapter, we present a computational study of multi-dimensional stochastic systems of differential equations. Especially competitive and evolutionary models. In these types of models, a certain number of uncertainties are causing side effects as random excitations and interactions. To numerically solve the considered systems, we propose the Itô-Taylor family schemes for multi-dimensional stochastic differential equations. Either for systems driven by one white noise or for systems having more than one source of excitations. A first-order accuracy is ensured in the approximation of double Itô integrals by using a truncation in the Fourier series expansion. To verify the accuracy of the proposed method, we consider a system of two stochastic differential equations with known analytical solution. Numerical results are presented for a reduced prototype system of the prebiotic evolutionary model.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-34702-4_13

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DOI: 10.1007/978-3-030-34702-4_13

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