On approximate analytical solutions of differential equations in enzyme kinetics using homotopy perturbation method

Vogt, Dietmar

doi:10.1007/s10910-012-0121-8

Cited by 10 publications

(4 citation statements)

References 11 publications

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“…In addition, he found that when the progress curves are analyzed by the direct solution of the integrated Michaelis-Menten equation, there were three different demonstrated approximations of W(x) with relatively high accuracy that are appropriate to utilize. In many studies, they studied this system and proposed many different kinds of approximate analytical solutions [5][6][7][8][9]. Hussam et al [10] investigated the semianalytical results of fractional time enzyme kinetics using the Laplace transformation and Adomian decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

Alqhtani

Saad

2021

Fractal Fract

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In this paper, three new models of fractal–fractional Michaelis–Menten enzymatic reaction (FFMMER) are studied. We present these models based on three different kernels, namely, power law, exponential decay, and Mittag-Leffler kernels. We construct three schema of successive approximations according to the theory of fractional calculus and with the help of Lagrange polynomials. The approximate solutions are compared with the resulting numerical solutions using the finite difference method (FDM). Because the approximate solutions in the classical case of the three models are very close to each other and almost matches, it is sufficient to compare one model, and the results were good. We investigate the effects of the fractal order and fractional order for all models. All calculations were performed using Mathematica software.

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Section: Introductionmentioning

confidence: 99%

Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

Alqhtani

Saad

2021

Fractal Fract

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“…This is used to calculate analytical approximate solutions for non-linear ODEs. The method is based on an assumption that a small parameter must exist in non-linear equations [7][8][9][10][11]. A homotopy perturbation method with two expanding parameters was suggested by [12].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Predator and Prey Model with some Computational Simulations

Khoshnaw¹

2017

J Appl Bioinforma Comput Biol

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Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species. Describing the dynamics of such models occasionally requires some techniques of model analysis. Choosing appropriate techniques of model analysis is often a difficult task. We define a prey (mouse) and predator (cat) model. The system is modelled by a pair of non-linear ordinary differential equations using mass action law, under constant rates. A proper scaling is suggested to minimize the number of parameters. More interestingly, we propose a homotopy technique with n expanding parameters for finding some analytical approximate solutions. Furthermore, using the local sensitivity method is another important step forward in this study because it helps to identify critical model parameters. Numerical simulations are provided using Matlab for different parameters and initial conditions.

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“…Yet, from a mathematical point of view, it is clear that analytical solutions take precedence whenever they can be found, so searching for them is not in vain. Actually, they can provide insight and conceptual novelty, which is impossible for numerical solutions, and analytical solutions for kinetic problems are still sought in an active field of research, both practically and theoretically [9,[15][16][17][18][19][20][21][22][23]. Such analytical solutions in dynamical systems are also viewed as highly valuable because the parameter dependence of the solution is much clearer that for a numerical solution.…”

Section: Introductionmentioning

confidence: 99%

Kinetics of irreversible consecutive processes with first order second steps: analytical solutions

Lente

2015

J Math Chem

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Analytical solutions are derived for a family of two-stage reactions, in which the later process is first order with respect to the product of the previous, non-first order step. A general strategy is shown that is suitable to handle typical cases. The strategy is demonstrated by considering, zeroth order, second order, mixed second order and third order initial reactions, analytical solutions for all of which can be obtained and advantageously used. The solutions can also be used as archetypes of intermediate formation and decay in chemical kinetics.

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On approximate analytical solutions of differential equations in enzyme kinetics using homotopy perturbation method

Cited by 10 publications

References 11 publications

Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

Dynamic Analysis of a Predator and Prey Model with some Computational Simulations

Kinetics of irreversible consecutive processes with first order second steps: analytical solutions

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