Open AccessA novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
Author(s) -
Zulqurnain Sabir,
Hafiz Abdul Wahab,
Juan Luis García Guirao
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022030
Subject(s) - pantograph , artificial neural network , sequential quadratic programming , nonlinear system , mathematics , mathematical optimization , computer science , function (biology) , correctness , differential equation , control theory (sociology) , algorithm , quadratic programming , artificial intelligence , mathematical analysis , engineering , mechanical engineering , physics , quantum mechanics , evolutionary biology , biology , control (management)
The present work is to solve the nonlinear singular models using the framework of the stochastic computing approaches. The purpose of these investigations is not only focused to solve the singular models, but the solution of these models will be presented to the extended form of the delayed, prediction and pantograph differential models. The Gudermannian function is designed using the neural networks optimized through the global scheme "genetic algorithms (GA)", local method "sequential quadratic programming (SQP)" and the hybridization of GA-SQP. The comparison of the singular equations will be presented with the exact solutions along with the extended form of delayed, prediction and pantograph based on these singular models. Moreover, the neuron analysis will be provided to authenticate the efficiency and complexity of the designed approach. For the correctness and effectiveness of the proposed approach, the plots of absolute error will be drawn for the singular delayed, prediction and pantograph differential models. For the reliability and stability of the proposed method, the statistical performances "Theil inequality coefficient", "variance account for" and "mean absolute deviation'' are observed for multiple executions to solve singular delayed, prediction and pantograph differential models.