A Numerical Method for Nonlinear Age-Structured Population Models with Finite Maximum Age
نویسندگان
چکیده
We propose a new numerical method for the approximation of solutions to a nonautonomous form of the classical Gurtin-Mac Camy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.
منابع مشابه
A Note on the Convergence of the Homotopy Analysis Method for Nonlinear Age-Structured Population Models
In this paper, a theorem is proved which presents the series solution obtained from the homotopy analysis method is convergent to the exact solution of nonlinear age-structured population models.
متن کاملApplication of the Second-kind Chebyshev Polynomials for the Nonlinear Age-structured Population Models
In this paper, we will introduce a method to find a numerical solution of nonlinear age-structured population model using second-kind Chebyshev polynomials. This method convert the nonlinear age-structured population models to an equivalent differential equation. We introduce two variable second-kind Chebyshev polynomials and their basic properties. These properties will be used to reduce the o...
متن کاملVariational iteration method for nonlinear age-structured population models
In this paper, we apply He’s variational iteration method (VIM) coupled with an auxiliary parameter which proves very effective to control the convergence region of an approximate solution. Moreover, a convenient way is considered for choosing a suitable auxiliary parameter via a residual function. The proposed algorithm is tested on some nonlinear age-structured population models, and numerica...
متن کاملAnalytic algorithms for Some Models of Nonlinear Age–Structured Population Dynamics and Epidemiology
Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and a...
متن کاملA Numerical Method for Spatial Diffusion in Age-Structured Populations
We propose a method to approximate numerically the diffusion of an age-structured population in a spatial environment. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. The method is implicit in time and, inside each time step, implicit in age. We provide stability and convergence results and we illustrate our appro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008