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Numerical Treatment of Multidimensional Stochastic, Competitive and Evolutionary Models

In: Disease Prevention and Health Promotion in Developing Countries

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  • Mostafa Zahri

    (University of Sharjah, College of Sciences)

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.

Suggested Citation

  • Mostafa Zahri, 2020. "Numerical Treatment of Multidimensional Stochastic, Competitive and Evolutionary Models," Springer Books, in: Abdesslam Boutayeb (ed.), Disease Prevention and Health Promotion in Developing Countries, chapter 0, pages 183-215, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-34702-4_13
    DOI: 10.1007/978-3-030-34702-4_13
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