Tan, C.S. (1985) Accurate Solution of Three Dimensional Poisson’s Equation in Cylindrical Coordinate by Expansion in Chebyshev Polynomials. Journal of Computational Physics, 59, 81-95.
http://dx.doi.org/10.1016/0021-9991(85)90108-1

has been cited by the following article:

• TITLE: High Accurate Fourth-Order Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate

  AUTHORS: Alemayehu Shiferaw, Ramesh Chand Mittal

  KEYWORDS: Poisson’s Equation; Tri-Diagonal Matrix; Fourth-Order Finite Difference Approximation; Hockney’s Method; Thomas Algorithm

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.4 No.2, March 21, 2014

  ABSTRACT: In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-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.