A New Basis for the Solution of the One-Dimensional Convection-Diffusion Equation Convection-Diffusion Equation

Stephen Brill & Stephen Brill
We present a family of functions that satisfy the one-dimensional convection-diffusion equation. This partial differential equation is widely used in the sciences and engineering, including to model the transport of contaminant dissolved in groundwater. Combinations of these functions are formed to satisfy boundary and initial conditions. The result is an inexpensive and highly accurate solution methodology.
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