| Summary: | A variety of finite difference schemes are explored for the numerical solution of elliptic partial differential equations, specifically the Poisson and convection-diffusion equations. Problems are investigated that require the use of a non-uniform or non-square mesh. This may be due to a non-square domain or a problem with a singularity. We explore the properties of the linear operators in the resulting systems of linear equations. In particular, we investigate the conditioning and eigenvalues of these operators, both numerically and in search of an approximation of these eigenvalues. We also investigate the choice of finite difference scheme with respect to accuracy and cost. === Science, Faculty of === Computer Science, Department of === Graduate
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