| publication name | Intelligent computing technique for solving singular multi-pantograph delay differential equation |
|---|---|
| Authors | Zulqurnain Sabir, Hafiz Abdul Wahab, Tri Gia Nguyen, Gilder Cieza Altamirano, Fevzi Erdoğan & Mohamed R. Ali |
| year | 2022 |
| keywords | |
| journal | |
| volume | Not Available |
| issue | Not Available |
| pages | Not Available |
| publisher | Not Available |
| Local/International | International |
| Paper Link | https://link.springer.com/article/10.1007/s00500-022-07065-0 |
| Full paper | download |
| Supplementary materials | Not Available |
Abstract
The purpose of this study is to introduce a stochastic computing solver for the multi-pantograph delay differential equation (MP-DDE). The MP-DDE is not easy to solve due to the singularities and pantograph terms. An advance computational intelligent paradigm is proposed to solve MP-DDE of the second kind by manipulating the procedures of the artificial neural networks (ANNs) through the optimization of genetic algorithm (GA) and sequential quadratic programming (SQP), i.e., ANNs-GA-SQP. A fitness function is constructed based on MP-DDE of second kind and corresponding boundary conditions. The correctness of the ANNs-GA-SQP is observed by performing the comparison of the proposed and exact solutions. The values of the absolute error (AE) in good measures are provided to solve the MP-DDE of the second kind. The efficacy and correctness of the stochastic computing approach to solve three problems of the MP-DDE of second kind to signify the efficiency, worth, and consistency. Moreover, the statistical soundings are applied to validate the accuracy and consistency.