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An Efficient Direct Method to Solve the Three Dimensional Poisson’s Equation

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DOI: 10.4236/ajcm.2011.14035    8,079 Downloads   15,678 Views   Citations

ABSTRACT

In this work, the three dimensional Poisson’s equation in Cartesian coordinates with the Dirichlet’s boundary conditions in a cube is solved directly, by extending the method of Hockney. The Poisson equation is approximated by 19-points and 27-points fourth order finite difference approximation schemes and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The efficiency 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. It is shown that 19-point formula produces comparable results with 27-point formula, though computational efforts are more in 27-point formula.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Shiferaw and R. Chand Mittal, "An Efficient Direct Method to Solve the Three Dimensional Poisson’s Equation," American Journal of Computational Mathematics, Vol. 1 No. 4, 2011, pp. 285-293. doi: 10.4236/ajcm.2011.14035.

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