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.