Numerical solution of homogeneous Smoluchowski's coagulation equation

Ranjbar, Mojtaba; Adibi, Hojatollah; Lakestani, Mehrdad

doi:10.1080/00207160802617012

Cited by 21 publications

(14 citation statements)

References 27 publications

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“…This equation is widely applied to describe the time evolution of the cluster-size distribution during aggregation processes. In this paper, the following Smoluchowski's equation [5,6], will be considered; ( , ) ( ) ( ), , ,…”

Section: Homogeneous Smoluchowski Coagulation Equationmentioning

confidence: 99%

New Method for Homogeneous Smoluchowski Coagulation Equation

H¹

2015

J Appl Computat Math

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Section: Homogeneous Smoluchowski Coagulation Equationmentioning

confidence: 99%

New Method for Homogeneous Smoluchowski Coagulation Equation

H¹

2015

J Appl Computat Math

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“…These series solution techniques offer results without making such assumptions. Some of the available strategies are Taylor polynomial and radial basis functions [18], Laplace-variational iteration method [19], ADM [20], HPM [21], optimal homotopy asymptotic method (OHAM) [22], HAM [23] and ODM [24]. Interestingly, some of the algorithm provided the closed form series solutions of coagulation equation (1.2) for the aggregation kernels K(x, y) = 1, x + y, xy and x…”

Section: Introductionmentioning

confidence: 99%

Elzaki Transform Based Accelerated Homotopy Perturbation Method for Multi-dimensional Smoluchowski's Coagulation and Coupled Coagulation-fragmentation Equations

Arora¹,

Kumar²,

Mammeri³

2023

Preprint

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This article aims to establish a semi-analytical approach based on the homotopy perturbation method (HPM) to find the closed form or approximated solutions for the population balance equations such as Smoluchowski's coagulation, fragmentation, coupled coagulation-fragmentation and bivariate coagulation equations. An accelerated form of the HPM is combined with the Elzaki transformation to improve the accuracy and efficiency of the method. One of the significant advantages of the technique lies over the classic numerical methods as it allows solving the linear and non-linear differential equations without discretization. Further, it has benefits over the existing semi-analytical techniques such as Adomian decomposition method (ADM), optimized decomposition method (ODM), and homotopy analysis method (HAM) in the sense that computation of Adomian polynomials and convergence parameters are not required. The novelty of the scheme is shown by comparing the numerical findings with the existing results obtained via ADM, HPM, HAM and ODM for non-linear coagulation equation. This motivates us to extend the scheme for solving the other models mentioned above. The supremacy of the proposed scheme is demonstrated by taking several numerical examples for each problem. The error between exact and series solutions provided in graphs and tables show the accuracy and applicability of the method. In addition to this, convergence of the series solution is also the key attraction of the work.

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“…The analytical solution for aggregation equation can be studied by many researchers for limited number of aggregation kernels. Ranjbar et al (2010) derived analytical solution for constant kernel using Taylor polynomials and radial basis functions. Moreover, Hammouch and Mekkaoui (2010) uses the Laplace-Variational iteration to obtain approximate series solution for equation (1.4).…”

Section: Introductionmentioning

confidence: 99%

Analytical approach for solving population balances: a homotopy perturbation method

Kaur

Singh

et al. 2019

J. Phys. A: Math. Theor.

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In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and boundary value problems without nonphysical restrictive assumptions such as linearization and discretization. It gives the solution in the form of series with easily computable solution components. The outcome of this study reveals that the proposed method can avoid numerical stability problems which often characterize in general numerical techniques related to this area. Several examples including Austin's kernel available in literature are examined to demonstrate the accuracy and applicability of the proposed method.

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Numerical solution of homogeneous Smoluchowski's coagulation equation

Cited by 21 publications

References 27 publications

New Method for Homogeneous Smoluchowski Coagulation Equation

New Method for Homogeneous Smoluchowski Coagulation Equation

Elzaki Transform Based Accelerated Homotopy Perturbation Method for Multi-dimensional Smoluchowski's Coagulation and Coupled Coagulation-fragmentation Equations

Analytical approach for solving population balances: a homotopy perturbation method

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