微分方程在西安市人口预测中的应用  

Application of Differential Equation in Population Prediction of Xi'an City

作　　者：唐贤芳[1] 刘小刚[2] 张如[1] 

机构地区：[1]西北工业大学明德学院,西安710124 [2]西北大学现代学院,西安710124

出　　处：《西安文理学院学报（自然科学版）》2017年第2期15-19,共5页Journal of Xi’an University(Natural Science Edition)

基　　金：陕西省教育厅专项科研计划项目(16JK2213)

摘　　要：利用中国统计网查得的2005年至2015年的西安市常住人口数量值,建立了西安市人口预测的三种微分模型即马尔萨斯模型、逻辑斯蒂增长模型及灰色预测GM(1,1)模型,对建立的灰色模型进行了精度检验.经过检验,可得所建立的灰色模型的精度为优,可以用于预测.并利用各模型对西安市的常住人口数量何时达到千万以及2060年的人口数量进行了预测.最后对各模型的优劣进行了比较,经过分析可得马尔萨斯模型仅适用于短期预测而其余两个模型均适用于中长期预测.In this paper,based on the number of permanent residents in Xi＇an city from 2005 to2015 in China statistics network,three differential models of population prediction in Xi＇an city were established,which is the Malthus model,Logistic model and grey prediction model GM（1,1）. The accuracy of the established gray models is tested,and after testing,the accuracy of the established grey models is excellent and can be used to do the population prediction.Each model is used to predict when will the number of permanent residents in Xi＇an city reach10 million and its population in 2060. Finally,the advantages and disadvantages of each model are compared,and the results show that the three models are suitable for short-term prediction,and the Malthus model is only suitable for short-term forecasting,while the other two models are suitable for the medium and long term prediction.

关 键 词：西安 马尔萨斯模型 逻辑斯蒂增长模型 灰色预测GM(1 1)模型 人口预测 

分 类 号：O29[理学—应用数学]