Open AccessAnalytical solution of coupled non-linear second order differential equations in enzyme kinetics
Author(s) -
Govindhan Varadharajan,
L. Rajendran
Publication year - 2011
Publication title -
natural science
Language(s) - English
Resource type - Journals
eISSN - 2150-4105
pISSN - 2150-4091
DOI - 10.4236/ns.2011.36063
Subject(s) - dimensionless quantity , reaction–diffusion system , perturbation (astronomy) , linear differential equation , differential equation , mathematics , mathematical analysis , homotopy perturbation method , kinetics , chemistry , thermodynamics , physics , homotopy , classical mechanics , pure mathematics , quantum mechanics
The coupled system of non-linear second-order reaction differential equation in basic enzyme reaction is formulated and closed analytical ex-pressions for substrate and product concentra-tions are presented. Approximate analytical me-thod (He’s Homotopy perturbation method) is used to solve the coupled non-linear differential equations containing a non-linear term related to enzymatic reaction. Closed analytical expres-sions for substrate concentration, enzyme sub-strate concentration and product concentration have been derived in terms of dimensionless reaction diffusion parameters k, and us-ing perturbation method. These results are compared with simulation results and are found to be in good agreement. The obtained results are valid for the whole solution domain