| publication name | Intelligent computing technique for solving singular multi-pantograph delay differential equation |
|---|---|
| Authors | Zulqurnain Sabir1 • Hafiz Abdul Wahab1 • Tri Gia Nguyen2 • Gilder Cieza Altamirano3 • Fevzi Erdog˘ an4 • Mohamed R. Ali5,6 |
| year | 2022 |
| keywords | |
| journal | Soft Computing |
| volume | 2022 |
| issue | Not Available |
| pages | Not Available |
| publisher | springer |
| Local/International | International |
| Paper Link | https://doi.org/10.1007/s00500-022-07065-0(0123456789().,-volV)(0123456789,-().volV) |
| 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.