E. H Chao, S. F. Paul, R. C. Davidson and K. S. Fine, “Direct Numerical Solution of Poisson’s Equation in Cylindrical (r, z) Coordinates,” Princeton University, Princeton, 1997.
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.