A Fast Stable Discretization of the Constant-Convection-Diffusion-Reaction Equations of Kinetic Capillary Electrophoresis (KCE)

TL;DR

This paper introduces a stable and fast discretization scheme for constant-convection-diffusion-reaction equations in kinetic capillary electrophoresis, improving computational efficiency while maintaining accuracy.

Contribution

It presents a novel discretization method leveraging constant convection velocity to ensure stability and speed, outperforming exact solution computations in certain cases.

Findings

The scheme is globally stable due to variable transformation.

Numerical algorithm is faster than exact solutions in tests.

The method maintains reasonable accuracy in simulations.

Abstract

A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables, which ensures the global stability of discretization. Convection-diffusion equations are notorious for their lack of stability, arising from the algebraic interaction of the convection and diffusion terms. Unexpectedly, our implemented numerical algorithm proves to be faster than computing exact solutions derived for a special case, while remaining reasonably accurate, as demonstrated in our runtime and error analysis.