Intelligent computing technique for solving singular multi-pantograph delay differential equation

Sabir Z., Wahab H. A., Nguyen T. G., Altamirano G. C., Erdoğan F., Ali M. R.

SOFT COMPUTING, vol.26, pp.6701-6713, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26
  • Publication Date: 2022
  • Doi Number: 10.1007/s00500-022-07065-0
  • Journal Name: SOFT COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Page Numbers: pp.6701-6713
  • Keywords: Pantograph, Stochastic computing, Artificial intelligence, Statistical soundings, Global scheme, Singular systems, Local search scheme, GENETIC-ALGORITHM, OPTIMIZATION, SYSTEMS, DESIGN
  • Van Yüzüncü Yıl University Affiliated: Yes


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.