A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times

Yadav, Nisha; Singh, Mehakpreet; Singh, Sukhjit; Singh, Rishabh; Kumar, Jitendra

doi:10.1016/j.chaos.2023.113628

Cited by 17 publications

(3 citation statements)

References 23 publications

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“…Several techniques are available in the literature to solve the PBEs numerically. Some popular methods are sectional methods, − method of moments, − semianalytical homotopy methods, and the Monte Carlo method. , A detailed review of these solution methods is available in ref . The Monte Carlo method is a probabilistic method that generates random numbers to obtain statistical approximations of the entities under consideration.…”

Section: Description Of the Process And State-of-the-artmentioning

confidence: 99%

See 1 more Smart Citation

Investigating Chemical Heterogeneity in Inclusion Populations: A Multivariate Population Balance Model Study in Gas-Stirred Ladles

Das,

Kroll-Rabotin,

Quatravaux

et al. 2023

Ind. Eng. Chem. Res.

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Section: Description Of the Process And State-of-the-artmentioning

confidence: 99%

“…Several techniques are available in the literature to solve the PBEs numerically. Some popular methods are sectional methods, 19−22 method of moments, 23−27 semianalytical homotopy methods, 28 and the Monte Carlo method. 29,30 A detailed review of these solution methods is available in ref 31.…”

Section: Description Of the Process And State-of-the-artmentioning

confidence: 99%

Investigating Chemical Heterogeneity in Inclusion Populations: A Multivariate Population Balance Model Study in Gas-Stirred Ladles

Das,

Kroll-Rabotin,

Quatravaux

et al. 2023

Ind. Eng. Chem. Res.

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“…The nonlinear collisional fragmentation problem presented in equation (1.1) has emerged as an increasingly significant topic within the scientific community. Numerous studies have explored various numerical methods and semi-analytical techniques for solving linear fragmentation and nonlinear aggregation models [11][12][13][14][15][16][17]. Singh et al have extensively discussed the limitations and advantages of different numerical techniques, including sectional methods, finite volume schemes and the Monte Carlo method [10,18].…”

Section: (A) Literature Review and Motivationmentioning

confidence: 99%

Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations

Yadav,

Das,

Singh

et al. 2023

Proc. R. Soc. A.

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The exploration of collisional fragmentation pheno-mena remains largely unexplored, yet it holds considerable importance in numerous engineering and physical processes. Given the nonlinear nature of the governing equation, only a limited number of analytical solutions for the number density function corresponding to empirical kernels are available in the literature. This article introduces a semi-analytical approach using the homotopy perturbation method to obtain series solutions for the nonlinear collisional fragmentation equation. The method presented here can be readily adapted to solve both linear and nonlinear integral equations, eliminating the need for domain discretization. To gain deeper insights intothe accuracy of the proposed method, a convergence analysis is conducted. This analysis employs the concept of contractive mapping within the Banach space, a well-established technique universally acknowledged for ensuring convergence. Various collisional kernels (product and polymerization kernels), breakage distribution functions (binary and multiple breakage) and various initial particle distributions are considered to obtain the new series solutions. The obtained results are successfully compared against finite volume method [26] solutions in terms of number density functions and their moments. The error between the exact and obtained series solutions is shown in plots and tables to confirm the applicability and accuracy of the proposed method.

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An efficient approach to obtain analytical solution of nonlinear particle aggregation equation for longer time domains

Yadav,

Singh,

Singh

et al. 2024

Advanced Powder Technology

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A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times

Cited by 17 publications

References 23 publications

Investigating Chemical Heterogeneity in Inclusion Populations: A Multivariate Population Balance Model Study in Gas-Stirred Ladles

Investigating Chemical Heterogeneity in Inclusion Populations: A Multivariate Population Balance Model Study in Gas-Stirred Ladles

Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations

An efficient approach to obtain analytical solution of nonlinear particle aggregation equation for longer time domains

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