一类人口发展问题的数值解

NUMERICAL SOLUTIONS TO THE POPULATION DEVELOPMENT PROBLEM

本文研究了只考虑自然生死因素的人口发展模型一类偏微分方程的初边值问题.建立了偏微分方程的差分格式,讨论了差分格式的相容性、收敛性和稳定性.以1996年的人口数据作为初始数据,通过对差分格式求解,得到了1996～2010年的每一年各年龄组的人口数和总人口数.结果表明:我国的人口总数在不断地增长,但增长速度渐趋缓慢;我国的人口年龄结构发生了变化,正由现在的成年型向老年型转化.

A population development model,a partial differential equation with a set of initial- boundary value problems, is built, in which only natural life-death factors are considered. The difference schemes are established and their compatibility, stability and convergence are discussed. With the data on population in 1996 regarded as the initial data ,various age groups＇ population and the gross population of the whole country in each year from 1996 to 2010 are calculated. As is expected, the gross population of our country is growing, but the growth rate is slowing down gradually,and the age-structure of population of our country is turning gradually from today＇s grown-up type into the old-age type.