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Numerical solution of a stochastic population growth model in a closed system. (English) Zbl 1444.65078

Summary: In this paper, we introduce a stochastic population model in a closed system. This model is a nonlinear stochastic integro-differential equation. At first, we solve this problem via the stochastic \(\theta\)-method. Then we solve it by using the Bernstein polynomials and collocation method. This method reduces integro-differential equation to a system of nonlinear algebraic equations. The results demonstrate applicability and accuracy of this method.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
34K50 Stochastic functional-differential equations
92D25 Population dynamics (general)
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