Bialecki, BernardWright, Lyndsey2007-01-032022-02-092014-12-012022-02-092013https://hdl.handle.net/11124/121962013 Fall.Includes bibliographical references (pages 30-31).We solve Poisson's Equation on the unit disc in polar coordinates using a fourth-order finite difference method. We use a half-point shift in the r direction, in order to avoid approximating the solution at r = 0. We derive a new fourth-order accurate finite difference method from analysis of the truncation error of the well-known second-order scheme. The resulting linear system is solved very efficiently (with cost almost proportional to the number of unknowns) using a combination of a Matrix Diagonalization Algorithm and Fast Fourier Transforms.born digitalmasters thesesengCopyright of the original work is retained by the author.Poisson's equationpolar coordinatesfourth-orderPoisson's equationFinite differencesCoordinates, PolarMatricesLinear systemsFourier transformationsText1-year embargo