基于POD方法带Poisson跳的随机扩散流行病模型数值模拟  

Numerical simulations based on POD for stochastic diffusion epidemic models with Poisson jumps

作　　者：杜玉龙[1] 李西宁[1] 张启敏[1,2] 

机构地区：[1]宁夏大学数学计算机学院,银川750021 [2]北方民族大学数学与信息科学学院,银川750021

出　　处：《应用数学与计算数学学报》2015年第3期338-354,共17页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11461053;11261043);宁夏自然科学基金资助项目(NZ12127)

摘　　要：将特征正交分解(proper orthogonal decomposition,简记为POD)方法结合有限元方法应用于带Poisson跳的扩散流行病模型,简化其为一个具有较低维数和较高精度的有限元格式,并给出POD有限元解和通常有限元解的误差分析.数值例子表明在POD有限元降维解和通常有限元解之间的误差足够小的情况下,POD有限元方法能大大地降低维数,提高计算速度和计算精度,从而验证带Poisson跳的随机扩散流行病模型的POD有限元格式是可行和有效的.We discuss a proper orthogonal decomposition（POD） method with the finite method for solving the stochastic diffusion epidemic models with Poisson jumps.We reduce the usual finite element（FE） formation into a reduced FE formation with lower dimensions and high enough accuracy and provide the estimates between the reduced POD FE solutions and the usual FE solutions.It is shown by numerical examples that the results of numerical computation are consistent with theoretical analysis.Moreover,it is also shown that this validates the feasibility and efficiency of the POD method.

关 键 词：特征正交分解 POISSON跳 误差分析 随机扩散流行病模型 

分 类 号：O211.63[理学—概率论与数理统计]