Sixth Order Compact Approximation with Completed Richardson Extrapolation

The sixth order compact approximation described in this article is a kind of Richardson extrapolation-based method, which uses two different scale grids to improve the order of accuracy of numerical solutions. Since the extrapolated solution with higher order accuracy is on the coarse grid, we consider to use completed Richardson extrapolation to get a higher order solution on the entire fine grid. Both truncation error analysis and numerical investigation are conducted to compare the proposed method and an existed Richardson extrapolation-based sixth order method with operator based interpolation.