Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method

Duan, Jun‐Sheng; Rach, Randolph; Wazwaz, Abdul‐Majid

doi:10.1007/s10910-014-0469-z

Cited by 35 publications

(17 citation statements)

References 20 publications

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“…experimentally studied absorption of carbon dioxide with the aid of a catalyst. (Duan, Rach, & Wazwaz, 2015;Duan & Rach, 2011) proposed the use of Adomian decomposition method for the simulation of the absorption of carbon dioxide into phenyl glycidyl ether. Theoretical analysis of mass transfer was given by Subramaniam et al (2012).…”

Section: Absorption Of Carbon Dioxide Into Phenyl Glycidyl Ethermentioning

confidence: 99%

“…4.2. The HAM for solving the absorption of CO2 by the PGE boundary value problem A model for steady state concentrations of carbon dioxide CO2 and PGE has been proposed as in Duan et al (2015) and Subramaniam et al (2012). The following system of two second order nonlinear ordinary differential equations representing the two chemicals must be solved:…”

Section: The Ham For Solving the Lane-emden Boundary Value Problemmentioning

confidence: 99%

“…with the following boundary conditions uð0Þ ¼ 1, uð1Þ ¼ k, v 0 ð0Þ ¼ 0 and vð1Þ ¼ 1: Here u(x) stands for the CO2 concentration and v(x) is the PGE concentration. The normalized system parameters are a 1 , a 2 , b 1 and b 2 : The carbon dioxide concentration at catalyst surface is denoted by k Finally, the dimensionless distance from the centre is x (Duan et al, 2015). Adomian (1994), Duan et al (2015), Biazar, Babolian, and Islam (2004), have used the Adomian decomposition method to develop a solution of this problem.…”

Section: The Ham For Solving the Lane-emden Boundary Value Problemmentioning

confidence: 99%

See 2 more Smart Citations

Boundary-domain integral method and homotopy analysis method for systems of nonlinear boundary value problems in environmental engineering

AL-Jawary

Rahdi

Ravnik

2020

Arab Journal of Basic and Applied Sciences

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In this paper we present the development of numerical methods for two problems in chemical engineering: adsorption of carbon dioxide into phenyl glycidyl ether and diffusion and reaction processes in a porous catalyst. Both problems are modelled by systems of two coupled nonlinear ordinary differential equations. Dirichlet and Neumann type boundary conditions are considered. We develop the standard homotopy analysis method and the boundary-domain element method to solve for the unknown steady-state concentrations of reactants. The validity of the proposed methods is checked and demonstrated by numerical examples. Convergence rates are compared and the advantages and drawbacks of the proposed methods are discussed and compared to the Mathematica NDSOLVE solver. We show, that the proposed homotopy analysis method features exponential convergence rate and is highly accurate and efficient. As low as 6 terms are needed to reach error norms of 10 À5 : Furthermore, the boundary-domain integral approach is also capable of solving the same problem very efficiently, using a very coarse computational mesh (21 nodes).

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Section: Absorption Of Carbon Dioxide Into Phenyl Glycidyl Ethermentioning

confidence: 99%

Section: The Ham For Solving the Lane-emden Boundary Value Problemmentioning

confidence: 99%

Section: The Ham For Solving the Lane-emden Boundary Value Problemmentioning

confidence: 99%

See 1 more Smart Citation

Boundary-domain integral method and homotopy analysis method for systems of nonlinear boundary value problems in environmental engineering

AL-Jawary

Rahdi

Ravnik

2020

Arab Journal of Basic and Applied Sciences

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show abstract

“…Also we calculate the error remainder with the maximal error remainder parameters and the approximate solution. The convenience function of the error remainder will be [15], [16]:…”

Section: Test Examplesmentioning

confidence: 99%

Analytic and numerical solution for duffing equations

AL-Jawary

Razaq

2016

IJBAS

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Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM ). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM ) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was M ATHEMATICA ® 9.0.

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“…Singla and Das [23] used ADM for solving a nonlinear problem involving conductive, convective and radiative stepped fin with temperature-dependent parameters. Duan et al [24] studied the concentrations of carbon dioxide absorbed into phenyl glycidyl ether using ADM. An analytical solution for the Schrödinger equation for Brownian motion in a double-well potential using ADM was presented by Ai-Jie et al [25]. Praveen and Rajendran [26] employed ADM and provided a solution to the problem of a reaction-diffusion process involved in packed bed photobioreactor.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

Noroozi¹,

Saedodin²,

Ganji³

2016

Archive of Mechanical Engineering

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The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

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Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method

Cited by 35 publications

References 20 publications

Boundary-domain integral method and homotopy analysis method for systems of nonlinear boundary value problems in environmental engineering

Boundary-domain integral method and homotopy analysis method for systems of nonlinear boundary value problems in environmental engineering

Analytic and numerical solution for duffing equations

Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

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