<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We identify sufficient conditions for the stability of some well-known finite difference schemes for the solution of the multivariable reaction-diffusion equations that model chemical reaction networks. Since the equations are mainly nonlinear, these conditions are obtained through local linearization. A recurrent condition is that the Jacobian matrix of the reaction part evaluated at some positive unknown solution is either D-semi-stable or semi-stable. We demonstrate that for a single reversible chemical reaction whose kinetics are monotone, the Jacobian matrix is D-semi-stable and therefore such schemes are guaranteed to work well.</p></abstract>

We identify sufficient conditions for the stability of some well-known finite difference schemes for the solution of the multivariable reaction-diffusion equations that model chemical reaction networks. Since the equations are mainly nonlinear, these conditions are obtained through local linearization. A recurrent condition is that the Jacobian matrix of the reaction part evaluated at some positive unknown solution is either D-semi-stable or semi-stable. We demonstrate that for a single reversible chemical reaction whose kinetics are monotone, the Jacobian matrix is D-semi-stable and therefore such schemes are guaranteed to work well.

On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networks

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

We identify sufficient conditions for the stability of some well-known finite difference schemes for the solution of the multivariable reaction-diffusion...

On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networks

Published Online: Dec 05, 2018

Page range: 121 - 140

Received: Oct 03, 2017

Accepted: Oct 08, 2018

DOI: https://doi.org/10.2478/caim-2018-0016

Keywords
Reaction-diffusion equations, Finite difference method, Stability, Amplification matrix, Linearization, Monotone kinetics

© 2018 Nathan Muyinda, et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networks

Published Online: Dec 05, 2018

Page range: 121 - 140

Received: Oct 03, 2017

Accepted: Oct 08, 2018

DOI: https://doi.org/10.2478/caim-2018-0016

KeywordsReaction-diffusion equations, Finite difference method, Stability, Amplification matrix, Linearization, Monotone kinetics

© 2018 Nathan Muyinda, et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Reaction-diffusion equations, Finite difference method, Stability, Amplification matrix, Linearization, Monotone kinetics