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.