Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value Problems
Fuzzy Differential Equations (FDEs) have attracted great interest among researchers. These FDEs have been used to develop a mathematical model for everyday life problems. In this study, we propose a solution method for a second-order Fuzzy Boundary Value Problem (FBVP). Four systems of FBVPs were de...
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241529?viewType=HTML |
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| author | Nurain Zulaikha Husin Muhammad Zaini Ahmad |
| author_facet | Nurain Zulaikha Husin Muhammad Zaini Ahmad |
| author_sort | Nurain Zulaikha Husin |
| collection | DOAJ |
| description | Fuzzy Differential Equations (FDEs) have attracted great interest among researchers. These FDEs have been used to develop a mathematical model for everyday life problems. In this study, we propose a solution method for a second-order Fuzzy Boundary Value Problem (FBVP). Four systems of FBVPs were developed based on the generalized fuzzy derivative. The second-order FBVP for each system was divided into two parts: Fuzzy non-homogeneous and fuzzy homogeneous equations. Using the shooting method, these two equations were then reduced to first-order FDEs. By implementing the Fuzzy Runge-Kutta Cash-Karp of the fourth-order method (FRKCK4), the approximate solution was compared with the analytical solution and the solution from the Fuzzy Runge-Kutta of the fourth-order method (FRK4). |
| format | Article |
| id | doaj-art-737a91ddb28c4f02a8ab5bfbcc93f22c |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-737a91ddb28c4f02a8ab5bfbcc93f22c2024-11-21T01:25:28ZengAIMS PressAIMS Mathematics2473-69882024-11-01911318063184710.3934/math.20241529Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value ProblemsNurain Zulaikha Husin0Muhammad Zaini Ahmad 1Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Perlis, MalaysiaInstitute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Perlis, MalaysiaFuzzy Differential Equations (FDEs) have attracted great interest among researchers. These FDEs have been used to develop a mathematical model for everyday life problems. In this study, we propose a solution method for a second-order Fuzzy Boundary Value Problem (FBVP). Four systems of FBVPs were developed based on the generalized fuzzy derivative. The second-order FBVP for each system was divided into two parts: Fuzzy non-homogeneous and fuzzy homogeneous equations. Using the shooting method, these two equations were then reduced to first-order FDEs. By implementing the Fuzzy Runge-Kutta Cash-Karp of the fourth-order method (FRKCK4), the approximate solution was compared with the analytical solution and the solution from the Fuzzy Runge-Kutta of the fourth-order method (FRK4).https://www.aimspress.com/article/doi/10.3934/math.20241529?viewType=HTMLfuzzy boundary value problemrunge-kutta cash-karpfuzzy differential equations |
| spellingShingle | Nurain Zulaikha Husin Muhammad Zaini Ahmad Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value Problems AIMS Mathematics fuzzy boundary value problem runge-kutta cash-karp fuzzy differential equations |
| title | Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value Problems |
| title_full | Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value Problems |
| title_fullStr | Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value Problems |
| title_full_unstemmed | Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value Problems |
| title_short | Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value Problems |
| title_sort | hybridization of the shooting and runge kutta cash karp methods for solving fuzzy boundary value problems |
| topic | fuzzy boundary value problem runge-kutta cash-karp fuzzy differential equations |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241529?viewType=HTML |
| work_keys_str_mv | AT nurainzulaikhahusin hybridizationoftheshootingandrungekuttacashkarpmethodsforsolvingfuzzyboundaryvalueproblems AT muhammadzainiahmad hybridizationoftheshootingandrungekuttacashkarpmethodsforsolvingfuzzyboundaryvalueproblems |