Numerical simulations based on POD for stochastic age-dependent system of two species (Q745992)

The authors consider a system of two species with age-dependent interaction, fertility rates, mortality rates, which is submitted to diffusion and stochastic external environment. They are interested in designing a simulation scheme for this system. As the usual Euler approximation scheme is quite expensive in terms of computational time, they turn to a finite elements (FE) method and in this framework they resort to the Galerkin proper orthogonal decomposition (POD) proposed by \textit{K. Kunisch} and \textit{S. Volkwein} [Numer. Math. 90, No. 1, 117--148 (2001; Zbl 1005.65112)]. They evaluate the effectt of the POD formulation in the FE approximation and provide an error estimate. Numerical examples illustrate the efficiency of the POD simulation method.