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

Alemayehu Shiferaw, Ramesh Chand Mittal

Department of Mathematics, Indian Institute of Technology, Roorkee, India.

DOI: 10.4236/ajcm.2014.42007                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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