Non-linear collision-induced breakage equation: finite volume and semi-analytical methods
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910365735976960 |
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| author | Bariwal, Sanjiv Kumar Hussain, Saddam Kumar, Rajesh |
| author_facet | Bariwal, Sanjiv Kumar Hussain, Saddam Kumar, Rajesh |
| contents | The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are investigated along with the well-known finite volume method (FVM) to comprehend the dynamical behavior of the non-linear system, i.e., the concentration function, the total number and the total mass of the particles in the system. The theoretical convergence analyses of the series solutions of HAM and AHPM are discussed. In addition, the error estimations of the truncated solutions of both methods equip the maximum absolute error bound. To justify the applicability and accuracy of these methods, numerical simulations are compared with the findings of FVM and analytical solutions considering three physical problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-linear collision-induced breakage equation: finite volume and semi-analytical methods Bariwal, Sanjiv Kumar Hussain, Saddam Kumar, Rajesh Numerical Analysis Analysis of PDEs The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are investigated along with the well-known finite volume method (FVM) to comprehend the dynamical behavior of the non-linear system, i.e., the concentration function, the total number and the total mass of the particles in the system. The theoretical convergence analyses of the series solutions of HAM and AHPM are discussed. In addition, the error estimations of the truncated solutions of both methods equip the maximum absolute error bound. To justify the applicability and accuracy of these methods, numerical simulations are compared with the findings of FVM and analytical solutions considering three physical problems. |
| title | Non-linear collision-induced breakage equation: finite volume and semi-analytical methods |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2403.08457 |