二维双曲方程基于POD方法的降阶有限差分外推迭代格式  

A POD-based reduced-order finite difference extrapolation iterative format for 2D hyperbolic equations

作　　者：腾飞[1] 罗振东[2] 李晓波[2] 

机构地区：[1]凯里学院数学科学学院,贵州凯里556011 [2]华北电力大学数理学院,北京102206

出　　处：《高校应用数学学报（A辑）》2014年第4期389-396,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11271127);贵州省教育厅自然科学研究项目(黔教合KY字[2013]207)

摘　　要：利用特征投影分解(POD)方法建立二维双曲型方程的一种基于POD方法的含有很少自由度但具有足够高精度的降阶有限差分外推迭代格式,给出其基于POD方法的降阶有限差分解的误差估计及基于POD方法的降阶有限差分外推迭代格式的算法实现.用一个数值例子去说明数值计算结果与理论结果相吻合.进一步说明这种基于POD方法的降阶有限差分外推迭代格式对于求解二维双曲方程是可行和有效的.A proper orthogonal decomposition （POD） technique is employed to establish a POD- based reduced-order finite difference extrapolation iterative format for two-dimensional （2D） hyperbolic equations, which includes very few degrees of freedom but holds sufficiently high accuracy. The error estimates of the POD-based reduced-order finite difference solutions and the algorithm implementation of the POD-based reduced-order finite difference extrapolation iterative format are provided. A numerical example is used to illustrate that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the POD-based reduced-order finite difference extrapolation iterative format is feasible and efficient for solving 2D hyperbolic equations.

关 键 词：特征投影分解 降阶有限差分外推迭代格式 双曲方程 

分 类 号：O242.21[理学—计算数学]