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Lynch, R.E. and Rice, J.R. (1978) High Accuracy Finite Difference Approximation to Solutions of Elliptic Partial Differential Equations. Proceedings of the National Academy of Sciences of the United States of America, 75, 2541-2544.
http://dx.doi.org/10.1073/pnas.75.6.2541

has been cited by the following article:

• TITLE: High Order Compact Difference Scheme and Multigrid Method for 2D Elliptic Problems with Variable Coefficients and Interior/Boundary Layers on Nonuniform Grids

  AUTHORS: Bin Lan, Yongbin Ge, Yan Wang, Yong Zhan

  KEYWORDS: Elliptic Equation, Coordinate Transformation, High Order Compact Difference Scheme, Multigrid Method, Interior/Boundary Layer

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.5, May 19, 2015

  ABSTRACT: In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.