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

Abstract

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.