On New Solutions of Fuzzy Hybrid Differential Equations by Novel Approaches
The goal of this paper is to find the best of two sixth-order methods, namely, RK-Huta and RK–Butcher methods for solving the fuzzy hybrid systems. We state a necessary definition and theorem in terms of consistency for convergence, and finally, we compare the obtained numerical results of two diffe...
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| Veröffentlicht in: | Journal of mathematics (Hidawi) Jg. 2023; S. 1 - 18 |
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| Sprache: | Englisch |
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2023
John Wiley & Sons, Inc Wiley |
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| Abstract | The goal of this paper is to find the best of two sixth-order methods, namely, RK-Huta and RK–Butcher methods for solving the fuzzy hybrid systems. We state a necessary definition and theorem in terms of consistency for convergence, and finally, we compare the obtained numerical results of two different methods with analytical solution using two different numerical examples. In addition to that, we generalize the solutions obtained by RK-6 Huta and RK-6 Butcher methods (same order different stage methods) for both the problems we handled. We are proposing these two methods in order to reduce the error in accuracy and to establish these two methods are better than any other existing numerical methods. The best of two sixth-order methods are found by the error analysis study for both the problems. Also, we show whether the change in number of stages of same order methods affects the accuracy of the approximation or not. |
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| AbstractList | The goal of this paper is to find the best of two sixth-order methods, namely, RK-Huta and RK–Butcher methods for solving the fuzzy hybrid systems. We state a necessary definition and theorem in terms of consistency for convergence, and finally, we compare the obtained numerical results of two different methods with analytical solution using two different numerical examples. In addition to that, we generalize the solutions obtained by RK-6 Huta and RK-6 Butcher methods (same order different stage methods) for both the problems we handled. We are proposing these two methods in order to reduce the error in accuracy and to establish these two methods are better than any other existing numerical methods. The best of two sixth-order methods are found by the error analysis study for both the problems. Also, we show whether the change in number of stages of same order methods affects the accuracy of the approximation or not. |
| Author | Thippan, Jayakumar Vadivel, R. Dhandapani, Prasantha Bharathi Hammachukiattikul, P. Unyong, Bundit |
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| Cites_doi | 10.1016/0165-0114(87)90029-7 10.1016/j.mcm.2006.09.014 10.1007/s00500-014-1314-9 10.1016/j.ins.2008.09.023 10.5890/dnc.2021.03.006 10.1016/0165-0114(86)90026-6 10.3390/electronics11091478 10.1016/0165-0114(87)90030-3 10.1016/j.nahs.2006.10.013 10.3389/fphy.2019.00168 10.1007/978-1-4684-3848-2_9 10.1016/s0019-9958(65)90241-x 10.1080/00207160802247620 10.1016/s0165-0114(97)00233-9 10.1016/j.jtusci.2014.06.002 10.1007/s00500-010-0659-y 10.5890/jand.2021.03.012 |
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| Copyright | Copyright © 2023 Prasantha Bharathi Dhandapani et al. Copyright © 2023 Prasantha Bharathi Dhandapani et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| References | 23 M. K. Jain (25) 1984 D. Prasantha Bharathi (6) 2019; 8 V. Lakshmikantham (8) 2003 10 11 12 T. Jayakumar (18) 2012; 6 13 A. Kandel (5) 1980 14 15 S. Pederson (17) 2008; 2 1 2 3 F. Saberiad (22) 2018; 12 4 A. Sepahvandzadeh (24) 2016; 10 V. Lakshmikantham (7) 1999; 5 9 T. Jayakumar (19) 2012; 6 20 S. Pederson (16) 2007; 45 21 |
| References_xml | – volume: 8 start-page: 520 issue: 9 year: 2019 ident: 6 article-title: Numerical solutions of fuzzy multiple hybrid single neutral delay differential equations publication-title: International Journal of Scientific &Technology Research – ident: 3 doi: 10.1016/0165-0114(87)90029-7 – volume: 45 start-page: 1133 year: 2007 ident: 16 article-title: Numerical solution to hybrid fuzzy systems publication-title: Mathematical and Computer Modelling doi: 10.1016/j.mcm.2006.09.014 – ident: 20 doi: 10.1007/s00500-014-1314-9 – volume: 6 start-page: 2619 year: 2012 ident: 19 article-title: Numerical solution for hybrid fuzzy system by Runge-Kutta Fehlberg method publication-title: International Journal of Mathematical Analysics – ident: 11 doi: 10.1016/j.ins.2008.09.023 – ident: 12 doi: 10.5890/dnc.2021.03.006 – ident: 4 doi: 10.1016/0165-0114(86)90026-6 – ident: 15 doi: 10.3390/electronics11091478 – volume-title: Numerical Solution of Differential Equations year: 1984 ident: 25 – volume-title: Theory of Fuzzy Differential Equations and Inclusions year: 2003 ident: 8 – ident: 23 doi: 10.1016/0165-0114(87)90030-3 – volume: 5 start-page: 9 year: 1999 ident: 7 article-title: Impulsive hybrid systems and stability theory publication-title: International Journal of Nonlinear Differential Equations – volume: 2 start-page: 626 year: 2008 ident: 17 article-title: The Runge-Kutta method for hybrid fuzzy differential equations publication-title: Nonlinear Analysis Hybrid Systems doi: 10.1016/j.nahs.2006.10.013 – ident: 10 doi: 10.3389/fphy.2019.00168 – start-page: 93 volume-title: Fuzzy Sets: Theory and Application to Policy Analysis and Information Systems year: 1980 ident: 5 article-title: Fuzzy dynamical systems and the nature of their solutions doi: 10.1007/978-1-4684-3848-2_9 – ident: 1 doi: 10.1016/s0019-9958(65)90241-x – ident: 13 doi: 10.1080/00207160802247620 – volume: 10 start-page: 75 issue: 4 year: 2016 ident: 24 article-title: Variational iternation method for solving hybri fuzzy differential equations publication-title: Journal of Mathematical Extension – ident: 2 doi: 10.1016/s0165-0114(97)00233-9 – volume: 12 start-page: 113 issue: 1 year: 2018 ident: 22 article-title: Application of homotopy perturbation methood for solving hybrid fuzzy differential equations publication-title: Journal of Mathematical Extension – ident: 9 doi: 10.1016/j.jtusci.2014.06.002 – ident: 21 doi: 10.1007/s00500-010-0659-y – ident: 14 doi: 10.5890/jand.2021.03.012 – volume: 6 start-page: 3591 year: 2012 ident: 18 article-title: Numerical solution for hybrid fuzzy system by Runge-Kutta method of order five publication-title: International Journal of Applied Mathematical Sciences |
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| Title | On New Solutions of Fuzzy Hybrid Differential Equations by Novel Approaches |
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