A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times
In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy p...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yadav, Nisha [verfasserIn] Singh, Mehakpreet [verfasserIn] Singh, Sukhjit [verfasserIn] Singh, Randir [verfasserIn] Kumar, Jitendra [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Chaos, solitons & fractals - Amsterdam [u.a.] : Elsevier Science, 1991, 173 |
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| Übergeordnetes Werk: |
volume:173 |
| DOI / URN: |
10.1016/j.chaos.2023.113628 |
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| Katalog-ID: |
ELV060483555 |
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| 100 | 1 | |a Yadav, Nisha |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times |
| 264 | 1 | |c 2023 | |
| 336 | |a nicht spezifiziert |b zzz |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
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| 520 | |a In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. | ||
| 650 | 4 | |a Coagulation equation | |
| 650 | 4 | |a Nonlinear integro-partial differential equation | |
| 650 | 4 | |a Homotopy perturbation method | |
| 650 | 4 | |a Pade approximation | |
| 650 | 4 | |a Finite volume scheme | |
| 700 | 1 | |a Singh, Mehakpreet |e verfasserin |0 (orcid)0000-0002-6392-6068 |4 aut | |
| 700 | 1 | |a Singh, Sukhjit |e verfasserin |4 aut | |
| 700 | 1 | |a Singh, Randir |e verfasserin |4 aut | |
| 700 | 1 | |a Kumar, Jitendra |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Chaos, solitons & fractals |d Amsterdam [u.a.] : Elsevier Science, 1991 |g 173 |h Online-Ressource |w (DE-627)314118497 |w (DE-600)2003919-0 |w (DE-576)094504040 |x 1873-2887 |7 nnns |
| 773 | 1 | 8 | |g volume:173 |
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| 936 | b | k | |a 30.20 |j Nichtlineare Dynamik |q VZ |
| 936 | b | k | |a 31.00 |j Mathematik: Allgemeines |q VZ |
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| 952 | |d 173 | ||
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30.20 31.00 |
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2023 |
| allfields |
10.1016/j.chaos.2023.113628 doi (DE-627)ELV060483555 (ELSEVIER)S0960-0779(23)00529-5 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Yadav, Nisha verfasserin aut A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. Coagulation equation Nonlinear integro-partial differential equation Homotopy perturbation method Pade approximation Finite volume scheme Singh, Mehakpreet verfasserin (orcid)0000-0002-6392-6068 aut Singh, Sukhjit verfasserin aut Singh, Randir verfasserin aut Kumar, Jitendra verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173 |
| spelling |
10.1016/j.chaos.2023.113628 doi (DE-627)ELV060483555 (ELSEVIER)S0960-0779(23)00529-5 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Yadav, Nisha verfasserin aut A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. Coagulation equation Nonlinear integro-partial differential equation Homotopy perturbation method Pade approximation Finite volume scheme Singh, Mehakpreet verfasserin (orcid)0000-0002-6392-6068 aut Singh, Sukhjit verfasserin aut Singh, Randir verfasserin aut Kumar, Jitendra verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173 |
| allfields_unstemmed |
10.1016/j.chaos.2023.113628 doi (DE-627)ELV060483555 (ELSEVIER)S0960-0779(23)00529-5 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Yadav, Nisha verfasserin aut A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. Coagulation equation Nonlinear integro-partial differential equation Homotopy perturbation method Pade approximation Finite volume scheme Singh, Mehakpreet verfasserin (orcid)0000-0002-6392-6068 aut Singh, Sukhjit verfasserin aut Singh, Randir verfasserin aut Kumar, Jitendra verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173 |
| allfieldsGer |
10.1016/j.chaos.2023.113628 doi (DE-627)ELV060483555 (ELSEVIER)S0960-0779(23)00529-5 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Yadav, Nisha verfasserin aut A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. Coagulation equation Nonlinear integro-partial differential equation Homotopy perturbation method Pade approximation Finite volume scheme Singh, Mehakpreet verfasserin (orcid)0000-0002-6392-6068 aut Singh, Sukhjit verfasserin aut Singh, Randir verfasserin aut Kumar, Jitendra verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173 |
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10.1016/j.chaos.2023.113628 doi (DE-627)ELV060483555 (ELSEVIER)S0960-0779(23)00529-5 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Yadav, Nisha verfasserin aut A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. Coagulation equation Nonlinear integro-partial differential equation Homotopy perturbation method Pade approximation Finite volume scheme Singh, Mehakpreet verfasserin (orcid)0000-0002-6392-6068 aut Singh, Sukhjit verfasserin aut Singh, Randir verfasserin aut Kumar, Jitendra verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173 |
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510 VZ 30.20 bkl 31.00 bkl A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times Coagulation equation Nonlinear integro-partial differential equation Homotopy perturbation method Pade approximation Finite volume scheme |
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ddc 510 bkl 30.20 bkl 31.00 misc Coagulation equation misc Nonlinear integro-partial differential equation misc Homotopy perturbation method misc Pade approximation misc Finite volume scheme |
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A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times |
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Yadav, Nisha |
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a note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times |
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A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times |
| abstract |
In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. |
| abstractGer |
In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. |
| abstract_unstemmed |
In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels. |
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