Open AccessNumerical investigations of the nonlinear smoke model using the Gudermannian neural networks
Author(s) -
Zulqurnain Sabir,
Muhammad Asif Zahoor Raja,
Abeer S. Alnahdi,
Mdi Begum Jeelani,
Mohamed Abdelkawy
Publication year - 2022
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.2022018
Subject(s) - nonlinear system , artificial neural network , correctness , genetic algorithm , computer science , smoke , fitness function , mathematical optimization , control theory (sociology) , mathematics , algorithm , artificial intelligence , engineering , physics , control (management) , quantum mechanics , waste management
These investigations are to find the numerical solutions of the nonlinear smoke model to exploit a stochastic framework called gudermannian neural works (GNNs) along with the optimization procedures of global/local search terminologies based genetic algorithm (GA) and interior-point algorithm (IPA), i.e., GNNs-GA-IPA. The nonlinear smoke system depends upon four groups, temporary smokers, potential smokers, permanent smokers and smokers. In order to solve the model, the design of fitness function is presented based on the differential system and the initial conditions of the nonlinear smoke system. To check the correctness of the GNNs-GA-IPA, the obtained results are compared with the Runge-Kutta method. The plots of the weight vectors, absolute error and comparison of the results are provided for each group of the nonlinear smoke model. Furthermore, statistical performances are provided using the single and multiple trial to authenticate the stability and reliability of the GNNs-GA-IPA for solving the nonlinear smoke system.