Jabbari Khanbehbin, Tahereh, Effati, Sohrab, Gachpazan, Mortaza, Miri, Seyed Mohsen. (1403). A new approach for solving delay differential equations with time varying delay. هنرهای کاربردی, 15(10), 235-241. doi: 10.22075/ijnaa.2023.31609.4681
Tahereh Jabbari Khanbehbin; Sohrab Effati; Mortaza Gachpazan; Seyed Mohsen Miri. "A new approach for solving delay differential equations with time varying delay". هنرهای کاربردی, 15, 10, 1403, 235-241. doi: 10.22075/ijnaa.2023.31609.4681
Jabbari Khanbehbin, Tahereh, Effati, Sohrab, Gachpazan, Mortaza, Miri, Seyed Mohsen. (1403). 'A new approach for solving delay differential equations with time varying delay', هنرهای کاربردی, 15(10), pp. 235-241. doi: 10.22075/ijnaa.2023.31609.4681
Jabbari Khanbehbin, Tahereh, Effati, Sohrab, Gachpazan, Mortaza, Miri, Seyed Mohsen. A new approach for solving delay differential equations with time varying delay. هنرهای کاربردی, 1403; 15(10): 235-241. doi: 10.22075/ijnaa.2023.31609.4681

A new approach for solving delay differential equations with time varying delay

International Journal of Nonlinear Analysis and Applications
مقاله 20، دوره 15، شماره 10، دی 2024، صفحه 235-241    اصل مقاله (417.86 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31609.4681
نویسندگان
Tahereh Jabbari Khanbehbin1؛ Sohrab Effati* 1، 2؛ Mortaza Gachpazan3؛ Seyed Mohsen Miri1
1Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
2Center of Excellence on Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran
3Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
چکیده
In this paper, Artificial Neural Networks are used to solve Delay Differential Equations. We have suggested an appropriate approximation function based on ANN and then by solving an optimization problem of error function, the neural network is trained. The advantage of this technique is that the proposed approximation functions, with a slight modification, can be used for most types of delay differential equations, including DDE with constant delay, time-dependent delay and pantograph delay. To demonstrate the effectiveness of the method, various examples have been tested and the validity and efficiency of the method have been shown.
کلیدواژه‌ها
Delay Differential Equations؛ Artificial Neural Networks؛ unconstrained optimization problem
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