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ANALYTICAL UPSTREAM COLLOCATION SOLUTION OF A FORCED STEADY-STATE CONVECTION-DIFFUSION EQUATION

Stephen H. Brill

Abstract


We give herein formulas for the solution of the Hermite collocation discretization of anonhomogeneoussteady-state convection-diffusion equation in one spatial dimension andwith constant coefficients,defined on a uniform mesh, with Dirichlet boundary conditions.The accuracy ofthe method is enhanced by employing ``upstream weighting'' of the convectiveterm in an optimal way.  We discuss also the issue of where to optimally samplethe forcing function.  Computational examples illustrate the efficacy of the optimalupstream weighting technique combined with optimal sampling of the forcing function.

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