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Title: An implicit, wiggle-free, and accurate upstream finite-difference algorithm for the one-dimensional transport-diffusion equation
Authors: Basco, David R.
Keywords: Algorithms
Equations--Numerical solutions
Diffusion--Mathematical models
Engineering mathematics
Difference equations
Publisher: Environmental Laboratory (U.S.)
Series/Report no.: Miscellaneous Paper;EL-84-4
Abstract: Abstract: A stable, accurate, and robust finite-difference algorithm has been successfully developed for engineering solution of the one-dimensional transport-diffusion equation. It is implicit and accurate to a higher order through removal of truncation errors, and uses quadratic upstream weighted differencing of the advection term to eliminate wiggle instabilities. Patterned after the explicit scheme, the implicit method essentially doubles the useful, stable range of application with comparable accuracy. Because of these significant improvements for one-dimensional problems, it is strongly recommended that the implicit method be extended to two dimensions.
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