In this thesis we present the exact solution to the Hermite collocation discretization of a quadratically forced steady-state convection-diffusion equation in one spatial dimension with constant coeffcients, defined on a uniform mesh, with Dirichlet boundary conditions. To improve the accuracy of the method we use upstream weightingu22 of the convective term in an optimal way. We also provide a method to determine where the forcing function should be optimally sampled. Computational examples are given, which support and illustrate the theory of the optimal sampling of the convective and forcing term.
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