Extended Parker–Sochacki method for Michaelis–Menten enzymatic reaction model

Abdelrazik, Ismail M.; Elkaranshawy, Hesham A.

doi:10.1016/j.ab.2015.11.017

Cited by 9 publications

(9 citation statements)

References 19 publications

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“…The Parker-Sochacki Method (PSM) [8] , [9] , [11] , [12] , [13] , [14] extends the conventional power series method to solving nonlinear initial value problems and initial value problems involving transcendental functions. The method relies on polynomial projection, which is described below.…”

Section: Basics Of the Proposed Methods (Multistage Parker-sochacki Mementioning

confidence: 99%

A new multistage technique for approximate analytical solution of nonlinear differential equations

Akindeinde

2020

Heliyon

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The article introduces a new multistage technique for solving a polynomial system of nonlinear initial and boundary value problems of differential equations. The radius of convergence R of the series solution to the problem is derived a-priorly in terms of the parameters of the polynomial system. Then guided by the convergence-control parameter , the domain of the problem is split into subintervals. By stepping out in a multistage manner, corresponding subproblems are defined which are then subsequently solved with conventional Parker-Sochacki method to get a piecewise continuous solution with very high accuracy. The method is applied to SIR epidemic model, stiff differential equation modelling combustion, Lorenz chaotic problem, and the Troesch's boundary value problem. The results obtained showed a remarkable accuracy when compared with Runge-Kutta Method of order 4. The article showcased the proposed method as a simple, yet accurate approximate analytical technique for nonlinear differential equations.

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Section: Basics Of the Proposed Methods (Multistage Parker-sochacki Mementioning

confidence: 99%

A new multistage technique for approximate analytical solution of nonlinear differential equations

Akindeinde

2020

Heliyon

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“…This result shows that the deactivation of the  COOH groups could suppress the interaction between the WO 3−x QDs and H 2 O 2 , indicating the COOH groups should play the role of binding sites of H 2 O 2 or TMB. 49 In addition, the linear relationship between the logarithm of the reaction rates and the reciprocal of the reaction temperature (290−330 K) was plotted based on the Arrhenius equation (Figure 5). 50 Information in detail was shown in the Supporting Information (S1.4).…”

Section: Recognition Of the Enzymatically Active And Inhibitivementioning

confidence: 99%

Recognition of the Enzymatically Active and Inhibitive Oxygenous Groups on WO_3–x Quantum Dots by Chemical Deactivation and Density Functional Theory Calculations

Liu

Gong

Wang

et al. 2020

ACS Appl. Bio Mater.

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The design and construction of efficient nanozymes are vital for bio/chemo-sensing applications, while the systematic catalytic mechanism study is the prerequisite. Tungsten oxide (WO3–x ) quantum dots (QDs), an alternative to conventional heavy metal-containing semiconductor QDs, possess peroxidase-like activity but limited catalytic efficiency. Therefore, the functions of the typical oxygenous groups in determining the enzymatic activity of the WO3–x QDs by target-specifically shielding the carboxyl (COOH), hydroxyl (OH), or carbonyl (CO) groups, respectively, using a chemical titration method. The results show that the CO groups could accelerate the nanozymatic catalysis kinetically, while the OH ones were the catalytically inhibitive sites, which were further corroborated by the density functional theory (DFT) computations. The application potential of the WO3–x derivatives with an enhanced catalytic ability was verified via the colorimetric cholesterol sensing. The proposed method based on the benzoic anhydride (BA)-modified WO3–x QDs with deactivated OH groups showed a wider linear range and higher sensitivity than those based on the unmodified ones.

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“…It is suitable for approximating a divergent series function. e approximant is derived by expanding the function as a ratio of two power series and determining both the numerator and denominator coefficients [28][29][30][31][32][33][34]. If we have a function f(u) that can be represented in a power series form as…”

Section: Laplace-padé Resummationmentioning

confidence: 99%

“…Power series solutions are first obtained for the system of ODE, and then, the Laplace-Padé resummation method (PSLP) is used to obtain the entailed approximate analytical solution. e technique used depends on the methodology developed in [27][28][29][30][31][32][33][34] for the general system of ODE. e solution is used for the analysis of the standard viral dynamic model of HCV after any type of DAA treatment initiation.…”

Section: Introductionmentioning

confidence: 99%

Innovative Approximate Analytical Solution for Standard Model of Viral Dynamics: Hepatitis C with Direct‐Acting Agents as an Implemented Case

Elkaranshawy

Ezzat

Abouelseoud

et al. 2019

Mathematical Problems in Engineering

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In this article, a novel approximate analytical solution is presented for solving the standard viral dynamic model. Basically, the standard model is used to study viral dynamics in patients for a wide range of viruses like HIV, HPV, HBV, and HCV. In this research work, the standard model for hepatitis C virus (HCV) is considered in detail; however, the analysis and results can be applicable for all other viruses. This standard model is used to study viral dynamics in patients treated with direct-acting antiviral agents (DAAs). Power series solution combined with Laplace–Padé resummation method (PSLP) is used to obtain the approximate analytical solutions for the model. To test the capability as well as the validity of the proposed method, results are compared with available viral load data published in the literature and with published simulation results. Good fits are obtained in the comparison for all cases considered. Given that medical specialists and physicians are more interested in solutions that yield direct and simple predictions, it is expected that the proposed approximate analytical solution would be attractive to them and help them to obtain a straightforward and a proper estimation regarding the viral load due to variations in treatment and/or patient’s parameters.

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Extended Parker–Sochacki method for Michaelis–Menten enzymatic reaction model

Cited by 9 publications

References 19 publications

A new multistage technique for approximate analytical solution of nonlinear differential equations

A new multistage technique for approximate analytical solution of nonlinear differential equations

Recognition of the Enzymatically Active and Inhibitive Oxygenous Groups on WO_3–x Quantum Dots by Chemical Deactivation and Density Functional Theory Calculations

Innovative Approximate Analytical Solution for Standard Model of Viral Dynamics: Hepatitis C with Direct‐Acting Agents as an Implemented Case

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Extended Parker–Sochacki method for Michaelis–Menten enzymatic reaction model

Cited by 9 publications

References 19 publications

A new multistage technique for approximate analytical solution of nonlinear differential equations

A new multistage technique for approximate analytical solution of nonlinear differential equations

Recognition of the Enzymatically Active and Inhibitive Oxygenous Groups on WO3–x Quantum Dots by Chemical Deactivation and Density Functional Theory Calculations

Innovative Approximate Analytical Solution for Standard Model of Viral Dynamics: Hepatitis C with Direct‐Acting Agents as an Implemented Case

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Recognition of the Enzymatically Active and Inhibitive Oxygenous Groups on WO_3–x Quantum Dots by Chemical Deactivation and Density Functional Theory Calculations