International Journal of Nonlinear Analysis and Applications

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

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

2 Center of Excellence on Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

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.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 10
October 2024
Pages 235-241
  • Receive Date: 09 August 2023
  • Revise Date: 27 September 2023
  • Accept Date: 29 November 2023