TITLE:
Analysis on Sixth-Order Compact Approximations with Richardson Extrapolation for 2D Poisson Equation
AUTHORS:
Ruxin Dai, Pengpeng Lin
KEYWORDS:
Richardson Extrapolation, Sixth-Order Solutions, High Order Compact Finite Difference Scheme, Truncation Error Analysis, 2D Poisson Equation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.6,
June
6,
2018
ABSTRACT: 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.