Mathematical Sciences: Monotone Numerical Methods for 2-D and 3-D Convection- Diffusion Equations

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This research program is concerned with the analysis, development and testing of finite difference methods for convection-diffusion problems in two and three dimensions based on the theory of monotone matrices. The algorithms developed will provide high accuracy, oscillation free, approximate solutions to these difficult problems in partial differential equations. The results of the research program will have direct applications in fluid flow, combustion and related problems.