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M. C. Lai and J. M. Tseng, “A Formally Fourth-Order Accurate Compact Scheme for 3D Poisson Equation in Cylindrical and Spherical Coordinates,” Journal of Computational and Applied Mathematics, Vol. 201, No. 1, 2007, pp. 175-181.
http://dx.doi.org/10.1016/j.cam.2006.02.011

has been cited by the following article:

• TITLE: Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates

  AUTHORS: Alemayehu Shiferaw, R. C. Mittal

  KEYWORDS: Poisson’s Equation; Hockney’s Method; Thomas Algorithm

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.4, December 20, 2013

  ABSTRACT: In this work, the three-dimensional Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly, by extending the method of Hockney. The Poisson equation is approximated by second-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.