Evaluation of the Einstein's strength of difference schemes for some chemical reaction-diffusion equations

TL;DR

This paper introduces a difference algebraic method to evaluate the Einstein's strength of difference schemes applied to chemical reaction-diffusion equations, enabling comparative analysis of their effectiveness.

Contribution

It presents a novel algebraic technique for assessing the Einstein's strength of difference schemes, specifically applied to reaction-diffusion equations in chemistry.

Findings

Finite-difference schemes for reaction-diffusion equations analyzed

Comparison of schemes based on Einstein's strength

Application to chromatography PDEs

Abstract

In this paper we present a difference algebraic technique for the evaluation of the Einstein's strength of a system of partial difference equations and apply this technique to the comparative analysis of difference schemes for chemical reaction-diffusion equations. In particular, we analyze finite-difference schemes for the Murray, Fisher, Burgers and some other reaction-diffusion equations, as well as mass balance PDEs of chromatography from the point of view of their strength.