随机固定资产模型有限元降维格式的数值解

Numerical Simulations Based on POD for a Class of Stochastic Age-Dependent Capital System

将特征正交分解(Proper Orthogonal Decomposition,简记为POD)方法应用于固定资产模型,简化其为一个具有较低维数和较高精度的有限元格式,并给出简化的有限元解的误差分析.数值例子表明在简化格式解和通常格式解之间的误差足够小的情况下,简化格式能大大的降低维数,提高计算速度和计算精度,从而验证固定资产模型的简化格式是可行和有效的.

The main aim of this paper is to apply proper orthogonal decomposition （POD） method to a usual finite element （FE） formulation for stochastic age-dependent capital system with real practical applied background, It is reduced into a reduced finite element formulation with lower dimensions and high accuracy. The error between the reduced POD FE solutions and the usual FE solutions are analyzed. Numerical examples shown that the reduced FE formulation based on POD approach can guarantees a sufficiently small errors between the reduced POD FE solutions and the usual FE solutions, Moreover, it is also shown that this validates the feasibility and efficiency of POD FE method.