Abstract A proper orthogonal decomposition (POD) technique is employed to establish a PODbased 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.
TENG Fei, LUO Zhen-dong, LI Xiao-bo. A POD-based reduced-order finite difference extrapolation iterative format for 2D hyperbolic equations. Applied Mathematics A Journal of Chinese Universities, 2014, 29(4): 389-396.
