非定常Burgers方程基于POD方法的全二阶差分格式降阶外推算法

利用特征投影分解方法和奇值分解技术对非定常Burgers 方程的经典全二阶有限差分格式做降阶处理, 给出一种时间和空间变量都是二阶精度的降阶差分格式, 并给出这种降阶全二阶精度差分解的误差估计和外推算法的实现, 最后用数值例子说明数值结果与理论结果是相吻合的.

A reduced-order extrapolation algorithm of fully second-order finite difference scheme for non-stationary Burgers equation

In this paper, a classical fully second-order finite difference scheme （FDS） for non-stationary Burgers equation is reduced with a proper orthogonal decomposition method and singular value decomposition technique. A reduced-order FDS of second-order accuracy about time and spacial variables is derived. The error estimates of the reduced-order FDS solutions and the implementation of its extrapolation algorithm are provided. Finally, a numerical example illustrates the fact that the results of numerical computation are consistent with theoretical conclusions.