scholarly journals Nonstandard finite difference schemes for Michaelis-Menten type reaction-diffusion equations

2012 ◽  
Vol 29 (1) ◽  
pp. 337-360 ◽  
Author(s):  
Michael Chapwanya ◽  
Jean M.-S. Lubuma ◽  
Ronald E. Mickens
Keyword(s):  
Finite Difference ◽  
Reaction Diffusion ◽  
Difference Schemes ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Finite Difference Schemes ◽  
Type Reaction ◽  
Nonstandard Finite Difference

scholarly journals A Comparison of Finite Difference Schemes for Computational Modelling of Biosensors

2007 ◽  
Vol 12 (3) ◽  
pp. 359-369 ◽  
Author(s):  
E. Gaidamauskaitė ◽  
R. Baronas
Keyword(s):  
Finite Difference ◽  
Computational Modelling ◽  
Computation Time ◽  
Reaction Diffusion ◽  
Difference Schemes ◽  
Reaction Diffusion Equations ◽  
Finite Difference Schemes ◽  
Enzymatic Reactions ◽  
Calculation Results ◽  
Kinetics Of

This paper presents a one-dimensional-in-space mathematical model of an amperometric biosensor. The model is based on the reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. The stated problem is solved numerically by applying the finite difference method. Several types of finite difference schemes are used. The numerical results for the schemes and couple mathematical software packages are compared and verified against known analytical solutions. Calculation results are compared in terms of the precision and computation time.

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

2018 ◽  
Vol 9 (1) ◽  
pp. 121-140
Author(s):  
Nathan Muyinda ◽  
Bernard De Baets ◽  
Shodhan Rao
Keyword(s):  
Finite Difference ◽  
Chemical Reaction ◽  
Jacobian Matrix ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Chemical Reaction Networks ◽  
Difference Schemes ◽  
Reaction Diffusion Equations ◽  
Reaction Networks ◽  
Finite Difference Schemes

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.

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