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Burg, C. and Erwin, T. (2009) Application of Richardson Extrapolation to the Numerical Solution of Partial Differential Equations. Numerical Methods for Partial Differential Equations, 25, 810-832.
https://doi.org/10.1002/num.20375

has been cited by the following article:

• 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.