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Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates

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DOI: 10.4236/ajcm.2013.34045    7,173 Downloads   11,413 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Shiferaw and R. Mittal, "Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates," American Journal of Computational Mathematics, Vol. 3 No. 4, 2013, pp. 356-361. doi: 10.4236/ajcm.2013.34045.

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