Author(s)

Ruxin Dai¹, Pengpeng Lin²

¹Department of Computer Science and Information Systems, University of Wisconsin River Falls, River Falls, WI, USA.
²Department of Mathematics, Statistics and Computer Science, University of Wisconsin Stout, Menomonie, WI, USA.

By using Richardson extrapolation and fourth-order compact finite difference scheme on different scale grids, a sixth-order solution is computed on the coarse grid. Other three techniques are applied to obtain a sixth-order solution on the fine grid, and thus give out three kinds of Richardson extrapolation-based sixth order compact computation methods. By carefully analyzing the truncation errors respectively on 2D Poisson equation, we compare the accuracy of these three sixth order methods theoretically. Numerical results for two test problems are discussed.

Richardson Extrapolation, Sixth-Order Solutions, High Order Compact Finite Difference Scheme, Truncation Error Analysis, 2D Poisson Equation

Dai, R. and Lin, P. (2018) Analysis on Sixth-Order Compact Approximations with Richardson Extrapolation for 2D Poisson Equation. Journal of Applied Mathematics and Physics, 6, 1139-1159. doi: 10.4236/jamp.2018.66097.