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Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates
Department of Mathematics, Indian Institute of Technology, Roorkee, India
Department of Mathematics, Indian Institute of Technology, Roorkee, India
- 1 Department of Mathematics, Indian Institute of Technology, Roorkee, India
- 2 Department of Mathematics, Indian Institute of Technology, Roorkee, India
American Journal of Computational Mathematics·Volume 03 (2013)·Pages 356–361·Published 21 November 2013·DOI10.4236/ajcm.2013.34045
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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.
KeywordsPoisson’s EquationHockney’s MethodThomas Algorithm
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