Research Of Numerical Solutions For Age-dependent Population System

The age-dependent population system has attracted a lot of attention in recent years.Therefore,it is extremely vital to get the numerical simulations.In this article,the numerical simulations of a class of age-dependent population systems is studied and the main contents are shown as followings.(1)In age-dependent population systems with diffusion item,a fourth-order Pad(?) numerical algorithm is proposed to calculate the population and the diffusion coefficient after a series of original form changes.It is proved that the forth-order Pad(?) numerical algorithm is unconditionally stable and has a truncation error of O(?t~2+ h~4).The obtained results can reflect the population and the diffusion coefficient more accurately,then,a numerical example is presented to demonstrate the efficiency and accuracy of the numerical method.(2)A class of stochastic age-dependent population system is studied by using Euler-Maruyama(EM)method,under linear growth condition,we discuss the asymptotic pth moment boundedness of the numerical solutions for stochastic age-dependent population system and establish a criterion for the asymptotical boundedness.After that,a numerical example is presented to demonstrate the accuracy of the conclusion.