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

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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.

References

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