Analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method

The mathematical modeling of nonlinear boundary value problems in catalytically chemical reactor is discussed. In this paper, we obtain the approximate analytical solution and the effectiveness factors for the evolution of single-step transformations under non-isothermal conditions using homotopy perturbation method. We have applied it to many reaction models and obtained very simple analytical expressions for the shape of the corresponding transformation rate peaks. These analytical solutions represent a significant simplification of the system’s description allowing easy curve fitting to experiment. The accuracy achieved with our method is checked against several reaction models and numerical results. A satisfactory agreement is noted.

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“…Case 1. When the reaction orders and , the analytical solution of (11) to (12) using homotopy perturbation method [35,[40][41][42][43][44] is…”

Section: Mathematical Formulation Of the Problem And Analysismentioning

confidence: 99%

Analytical Solution of Non-Isothermal Diffusion-Reaction Processes and Effectiveness Factors

Ananthaswamy¹,

Rajendran²

2013

ISRN Physical Chemistry

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“…Ji Huan He used the HPM to solve the light hill equation [20], the Duffing equation [21] and the Blasius equation [22]. The idea has been used to solve non-linear boundary value problems, integral equations and many other problems [23][24][25][26][27]. The HPM is unique in its applicability, accuracy and efficiency.…”

Section: Analytical Expressions Of Concentrations Using Homotopy Pertmentioning

confidence: 99%

Analytical expression of concentrations of adsorbed CO molecules, O atoms and oxide oxygen

Thangapandi¹,

Rajendran²

2013

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A mathematical model of the oscillatory regimes of CO oxidation over plantinum-group metal catalysts are discussed. The model is based on nonstationary diffusion equation containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents the analytical and numerical solution of the system of non-linear differential equations. Here the Homotopy perturbation method (HPM) is used to find out the analytical expressions of the concentration of CO molecules, O atom and oxide oxygen respectively. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical and numerical results is observed.

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“…Mathematical modeling of enzyme kinetics is given in the books by Rubinow [10], Murray [11], Segel [12] and Roberts [13]. Recently Rajendran and his team also solved some non linear problems in enzyme reaction kinetics [14][15][16][17][18][19]. The purpose of this communication is to derive asymptotic approximate expressions for the concentration of substrate and product in enzyme inhibition process.…”

Section: Introductionmentioning

confidence: 99%

Analytical expressions of the concentrations of substrate and product in enzyme inhibition process

Muthukumar¹,

Rajendran²

2013

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The initial and boundary value problem in enzyme reactions mechanism for inhabitation process is discussed. Approximate analytical expressions for the concentrations of substrate and product are presented. Approximate analytical solutions of non-linear reaction equations containing non-linear terms related to enzymatic reaction mechanism are solved using Homotopy perturbation method. The relevant analytical expression for the substrate and product concentration profiles is discussed in terms of dimensionless reaction diffusion parameters α, β, γ_E, and γ_S. Numerical solution is also obtained using Matlab program. Our analytical expression compared with numerical estimation and good agreement is noted

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Analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method

Cited by 28 publications

References 26 publications

Analytical Solution of Non-Isothermal Diffusion-Reaction Processes and Effectiveness Factors

Analytical Solution of Non-Isothermal Diffusion-Reaction Processes and Effectiveness Factors

Analytical expression of concentrations of adsorbed CO molecules, O atoms and oxide oxygen

Analytical expressions of the concentrations of substrate and product in enzyme inhibition process

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