Akbari-Ganji's Method (AGM) for solving non-linear reaction - Diffusion equation in the electroactive polymer film

Dharmalingam, K. M.; Veeramuni, M.

doi:10.1016/j.jelechem.2019.04.061

Cited by 26 publications

(7 citation statements)

References 18 publications

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“…The efficiency of the AGM solution is compared with the HPM solution, demonstrating the advantages of the AGM method [19]. We esteem the report on the AGM proposed by Dharmalingam et al [20], which was submitted recently.…”

Section: Introductionmentioning

confidence: 81%

A study on various types of immobilization of enzyme kinetic mechanisms by comparing with the solutions obtained from AGM and MADM

Saravanakumar,

Veeramuni,

Veeramani

et al. 2024

Preprint

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In this article, the kinetic mechanisms are based on Michaelis-Menten reaction in presence of substrate inhibition have been solved by techniques ‘Akbari-Ganji’s Method’ (AGM) and ‘Modified Adomian decomposition method’ (MADM). Comparisons of solution of dimensionless substrate and product concentrations for various kinetic mechanisms have been carried out using AGM, MADM and numerical simulation. We assessed the impact of Thiele modulus, dimensionless inhibition degree, and concentration of substances outside the support on changing nature of substrate and product concentrations within the boundary layer in this study. The obtained results depict that the used methods have good accuracy for different values of kinetic parameters. Furthermore, the mean integrated effectiveness factor has been derived for all the mechanisms employing AGM solutions. This paper clearly illustrates the distinctions between MADM and AGM.

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Section: Introductionmentioning

confidence: 81%

A study on various types of immobilization of enzyme kinetic mechanisms by comparing with the solutions obtained from AGM and MADM

Saravanakumar,

Veeramuni,

Veeramani

et al. 2024

Preprint

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“…In the AGM, nonlinear differential equations are converted to a set of nonlinear algebraic equations through choosing a proper answer function. The function contains constant coefficients, which are computed by the AGM [25,26,27]. To describe the general procedure of the AGM, the n th-order nonlinear differential equation is assumed to be…”

Section: Hybrid Methodsmentioning

confidence: 99%

“…Solving Equations (9) and (10), the final solutions to the nonlinear differential (6) are reached as an algebraic function [25–27].…”

Section: Hybrid Methodsmentioning

confidence: 99%

A study on an incompressible polymeric pressurized vessel subjected to bulk degradation

Kazemian

Goudarzi

Hassani

2021

Mathematics and Mechanics of Solids

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To study the mechanical behavior of an incompressible polymeric degradable vessel subjected to the neo-Hookean constitutive model, two solution frameworks are introduced. One is combining a recently developed semi-analytical method and the [Formula: see text]-family time approximation (hybrid method). The other is the Standard Galerkin Finite Element Method (SGFEM), which is implemented by providing a script in the FlexPDE commercial software. A deformation-induced evolution law is used to study the dependence of material properties upon time and position in the polymeric vessel during bulk degradation. The convergence of the two proposed methods on degradable vessel responses under the axisymmetric plane-strain conditions is seen. Although the hybrid method, unlike the SGFEM, is implemented as an iteration-based algorithm, it uses highly acceptable central processing unit time because it can directly solve differential equations without converting variables. The FlexPDE method is much easier to extend to more complex case studies because the hybrid method is based on an analytical approach. It is found that less pressure is required to maintain the incompressibility of the material during the degradation. The material response to incompressibility decreases more sharply in the inner radius of the vessel. Initially, the hoop stress decreases in the inner radius but eventually reaches more than its virgin value.

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“…are applied to solve the nonlinear problems. In this paper, Akbari-Ganji's method is applied to find the analytical expression for the concentration of the glucose [6,14]. The approximate analytical expression for glucose concentration using Akbari-Ganji's method is given by…”

Section: Analytical Solution Of the Glucose Concentration And Current...mentioning

confidence: 99%

Approximate Analytical Solution to a Pore Network Model of Deactivation of Immobilized Glucose Isomerase in Packed-Bed Reactors Using Akbari-Ganji’s Method

Seethalakshmi¹,

Ananthaswamy²,

Narmatha

et al. 2022

Comm. Math. Appl.

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The main objective of this paper is to derive an approximate analytical solution for the mathematical model pertaining to deactivation of immobilized glucose in packed-bed reactors. The Akbari-Ganji's method is applied to solve the previously developed mathematical model. The approximate analytical expressions corresponding to the concentration and current in the steady state condition have been derived for all values of parameters. Excellent agreement is obtained between the analytical solution and the numerical simulation. The analytical solution presented in this paper is presented for the first time. The results of this work will provide a better understanding of the mathematical model examined.

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Akbari-Ganji's Method (AGM) for solving non-linear reaction - Diffusion equation in the electroactive polymer film

Cited by 26 publications

References 18 publications

A study on various types of immobilization of enzyme kinetic mechanisms by comparing with the solutions obtained from AGM and MADM

A study on various types of immobilization of enzyme kinetic mechanisms by comparing with the solutions obtained from AGM and MADM

A study on an incompressible polymeric pressurized vessel subjected to bulk degradation

Approximate Analytical Solution to a Pore Network Model of Deactivation of Immobilized Glucose Isomerase in Packed-Bed Reactors Using Akbari-Ganji’s Method

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