%0 Journal Article
%T Fast Finite Difference Solutions of the Three Dimensional Poisson¡¯s Equation in Cylindrical Coordinates
%A Alemayehu Shiferaw
%A R. C. Mittal
%J American Journal of Computational Mathematics
%P 356-361
%@ 2161-1211
%D 2013
%I Scientific Research Publishing
%R 10.4236/ajcm.2013.34045
%X <p style=\"text-align:justify;\">
	<span>In this work, the <a name=\"OLE_LINK1\"></a>three</span><span>-</span><span>dimensional</span><span> Poisson¡¯s equation in cylindrical coordinates system with the Dirichlet¡¯s boundary conditions in a portion of a cylinder for <span>is solved directly, by extending the method of Hockney. The Poisson equation is approximated by second</span><span>-</span><span>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.</span><span></span></span> 
</p>
%K Poisson¡¯s Equation
%K Hockney¡¯s Method
%K Thomas Algorithm
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=40966