Steady-state current in product inhibition kinetics in an amperometric biosensor: Adomian decomposition and Taylor series method

Rani, R. Usha; Rajendran, L.; Lyons, Michael E. G.

doi:10.1016/j.jelechem.2021.115103

Cited by 20 publications

(3 citation statements)

References 42 publications

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“…to solve nonlinear problems in chemistry [48][49][50][51][52][53]. By applying this approach to the nonlinear Eqs.…”

Section: Analytical Solution Using the Taylor's Series Methodsmentioning

confidence: 99%

Approximate Analytical Solutions for Nonlinear Reaction-Diffusion Equations at Conducting Polymer Modified Ultramicroelectordes via Taylor’s Series Method

Yokeswari,

Jayasimman,

Lynons

et al. 2023

Preprint

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The primary goal of this article is to present novel analytical solutions for the coupled nonlinear equation found in polymer-modified conducting ultramicroelectrodes. Taylor's series method is utilized to obtain approximate analytical solutions for the reaction-diffusion equations, allowing for the determination of the substrate and mediator concentrations as well as the current response in relation to the substrate concentration at the electrode's surface. The impact of different factors on concentration and current is also explored. Our analytical findings exhibit a satisfactory degree of correspondence when compared to both numerical results obtained via MATLAB and prior analytical outcomes. Mathematics Subject Classification 34B60. 65L10. 82D60

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“…to solve nonlinear problems in chemistry [48][49][50][51][52][53]. By applying this approach to the nonlinear Eqs.…”

Section: Analytical Solution Using the Taylor's Series Methodsmentioning

confidence: 99%

Approximate Analytical Solutions for Nonlinear Reaction-Diffusion Equations at Conducting Polymer Modified Ultramicroelectordes via Taylor’s Series Method

Yokeswari,

Jayasimman,

Lynons

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Recent techniques for solving non-linear differential equations include using hyperbolic functions [21][22], Taylor's series approach [23][24], Adomian decomposition method [25], the homotopy analysis method [26], and variational iteration method [27]. Among these techniques, Ji-Huan's homotopy perturbation method (HPM) uses the linearization process to solve nonlinear equations [28][29][30].…”

Section: An Approximative Analytical Expression For the Concentration...mentioning

confidence: 99%

Mathematical Investigation of Non-Linear Reaction-Diffusion Equations on Multiphase Flow Transport in the Entrapped-Cell Photobioreactor Using Asymptotic Methods

Reena,

Swaminathan

2024

Int. J. Anal. Appl.

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The mathematical investigation of a multiphase flow transport model intended to clarify the interaction mechanism between reactions and diffusion processes in the gel granules containing the entrapped-cell photobioreactor Rhodopseudomonas palustris CQK 01 is presented in this research. The model uses two pertinent non-linear reaction-diffusion equations for biochemical interactions in the photobioreactor under steady-state circumstances to reflect the substrate and product concentration within the gel granules. The solid phase and liquid phase fluxes within the gel granules and their concentrations are analytically calculated using the asymptotic methods of the Akbari-Ganji method and the homotopy perturbation approach. Our analytical results and the numerical data obtained by MATLAB software are compared to determine accuracy. The analytical results agreed with the simulated results for all possible reaction-diffusion and saturation parameter values. In addition, the impacts of applying two limiting cases—saturated and unsaturated enzyme kinetics—were examined. The close correspondence between the simulated and analytical data demonstrates that the parameters in our suggested solution can be used to simulate the dynamic performance of a system.

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“…Non-linear problems are highly complex to solve analytically. Recently several analytical techniques have been used to solve non-linear equations like Homotopy Perturbation Method(HPM), the Variational iteration method, Taylor's series method(TSM) , the Akbari-Ganji method and the Hyperbolic function method [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Here we employed two methods HPM and TSM to solve Eqns(11-13).…”

Section: Analytical Observationsmentioning

confidence: 99%

Mathematical Modelling and Application of Analytical Methods for A Non-Linear EC2E Mechanism in Rotating Disk Electrode

Nebiyal,

Swaminathan,

Karpagavalli

2024

Int. J. Anal. Appl.

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Rotating disk electrode is the hydrodynamic technique used in the process of analyzing electroanalytic works. This paper deals with the mathematical model describing a non-linear EC2E mechanism that arises in a rotating disk electrode. This model is based on the system of non-linear reaction-convection-diffusion equations. EC2E mechanism has an application in finding the shape of current curves in the system of chronoamperometry in addition to steady-state voltammetry. The approximate analytical expression for the concentration of reactant species and current at steady-state condition is obtained using the analytical methods. The attained analytical result is compared with the numerical simulation (MATLAB) result. A satisfactory result is obtained between the series of solutions. The influence of parameters on the concentration of species and current is investigated and presented graphically.

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Steady-state current in product inhibition kinetics in an amperometric biosensor: Adomian decomposition and Taylor series method

Cited by 20 publications

References 42 publications

Approximate Analytical Solutions for Nonlinear Reaction-Diffusion Equations at Conducting Polymer Modified Ultramicroelectordes via Taylor’s Series Method

Approximate Analytical Solutions for Nonlinear Reaction-Diffusion Equations at Conducting Polymer Modified Ultramicroelectordes via Taylor’s Series Method

Mathematical Investigation of Non-Linear Reaction-Diffusion Equations on Multiphase Flow Transport in the Entrapped-Cell Photobioreactor Using Asymptotic Methods

Mathematical Modelling and Application of Analytical Methods for A Non-Linear EC2E Mechanism in Rotating Disk Electrode

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