基于POD方法随机两种群系统的数值解讨论  

Numerical Simulations Based on POD for Stochastic Age-dependent Population

作　　者：顾银鲁[1] 冯娟婷 李西宁[2] 张启敏[2] 

机构地区：[1]银川能源学院基础部,宁夏银川750105 [2]宁夏大学数学与计算机学院,宁夏银川750021

出　　处：《数学的实践与认识》2016年第23期143-154,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11461053;11261043)

摘　　要：主要目的是将特征正交分解(Proper Orthogonal Decomposition,简记为POD)方法应用于随机两种群系统,Euler方法是研究和讨论随机两种群系统数值解最有效的一种方法,但是这种方法存在计算时间久,自由度大等缺点.因此考虑POD方法,使其成为一个具有较低维数和较高精度的有限元格式.并给出了简化的有限元解的误差分析,通过数值算例进一步验证了随机两种群系统的POD FE(Finite Element,简记为FE)方法是可行和有效的.The main aim of this paper is to investigate the numerical simulations based on proper or- thogonal decomposition （POD） for stochastic age-dependent population system of two species. The Euler approximate method are invaluable tools for stochastic age-dependent population system of two species. However, they cost high computational times and memory requirements when dealing with Stochastic Age-dependent Population system of two species. In this paper, we consider POD method. It is reduced into a reduced finite element （FE） formulation with lower dimensions and high enough accuracy. The error estimates between the reduced POD FE solutions and the usual FE solutions are provided. A numerical example to shown the POD simulations method are feasible and efficacy for stochastic age-dependent population system of two species.

关 键 词：随机两种群系统 误差 有限元格式 特征正交分解法 

分 类 号：O241.82[理学—计算数学]