Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method
We develop the Fuzzy Improved Runge-Kutta Nystrom (FIRKN) method for solving second-order fuzzy differential equations (FDEs) based on the generalized concept of higher-order fuzzy differentiability. The scheme is two-step in nature and requires less number of stages which leads to less number of fu...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30889/ http://psasir.upm.edu.my/id/eprint/30889/1/Numerical%20solution%20of%20second.pdf |
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| author | Rabiei, Faranak Ismail, Fudziah Ahmadian, Ali Salahshour, Soheil |
| author_facet | Rabiei, Faranak Ismail, Fudziah Ahmadian, Ali Salahshour, Soheil |
| author_sort | Rabiei, Faranak |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We develop the Fuzzy Improved Runge-Kutta Nystrom (FIRKN) method for solving second-order fuzzy differential equations (FDEs) based on the generalized concept of higher-order fuzzy differentiability. The scheme is two-step in nature and requires less number of stages which leads to less number of function evaluations in comparison with the existing Fuzzy Runge-Kutta Nystrom method. Therefore, the new method has a lower computational cost which effects the time consumption. We assume that the fuzzy function and its derivative are Hukuhara differentiable. FIRKN methods of orders three, four, and five are derived with two, three, and four stages, respectively. The numerical examples are given to illustrate the efficiency of the methods. |
| first_indexed | 2025-11-15T09:08:34Z |
| format | Article |
| id | upm-30889 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:08:34Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-308892015-10-30T03:10:28Z http://psasir.upm.edu.my/id/eprint/30889/ Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method Rabiei, Faranak Ismail, Fudziah Ahmadian, Ali Salahshour, Soheil We develop the Fuzzy Improved Runge-Kutta Nystrom (FIRKN) method for solving second-order fuzzy differential equations (FDEs) based on the generalized concept of higher-order fuzzy differentiability. The scheme is two-step in nature and requires less number of stages which leads to less number of function evaluations in comparison with the existing Fuzzy Runge-Kutta Nystrom method. Therefore, the new method has a lower computational cost which effects the time consumption. We assume that the fuzzy function and its derivative are Hukuhara differentiable. FIRKN methods of orders three, four, and five are derived with two, three, and four stages, respectively. The numerical examples are given to illustrate the efficiency of the methods. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30889/1/Numerical%20solution%20of%20second.pdf Rabiei, Faranak and Ismail, Fudziah and Ahmadian, Ali and Salahshour, Soheil (2013) Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method. Mathematical Problems in Engineering, 2013. art. no. 803462. pp. 1-10. ISSN 1024-123X; ESSN: 1563-5147 http://www.hindawi.com/journals/mpe/2013/803462/ 10.1155/2013/803462 |
| spellingShingle | Rabiei, Faranak Ismail, Fudziah Ahmadian, Ali Salahshour, Soheil Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method |
| title | Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method |
| title_full | Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method |
| title_fullStr | Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method |
| title_full_unstemmed | Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method |
| title_short | Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nystrom method |
| title_sort | numerical solution of second-order fuzzy differential equation using improved runge-kutta nystrom method |
| url | http://psasir.upm.edu.my/id/eprint/30889/ http://psasir.upm.edu.my/id/eprint/30889/ http://psasir.upm.edu.my/id/eprint/30889/ http://psasir.upm.edu.my/id/eprint/30889/1/Numerical%20solution%20of%20second.pdf |