Gudermannian Neural Networks for Two-Point Nonlinear Singular Model Arising in the Thermal-Explosion Theory

• Published in: Neural processing letters Vol. 56; no. 4; p. 206
• Main Authors: Fatima, Samara, Sabir, Zulqurnain, Baleanu, Dumitru, Alhazmi, Sharifah E.
• Format: Journal Article
• Language: English
• Published: New York Springer US 26.06.2024; Springer Nature B.V
• Subjects: Approximation; Artificial Intelligence; Boundary value problems; Complex Systems; Computational Intelligence; Computer Science; Error functions; Explosions; Genetic algorithms; Methods; Neural networks; Neurons; Optimization techniques; Quadratic programming; Statistical analysis; Singular; Nonlinear; Two-points; Genetic algorithm; Thermal explosion; Complexity
• ISSN: 1573-773X; 1370-4621; 1573-773X
• DOI: 10.1007/s11063-024-11512-4

The goal of this research is to design the Gudermannian neural networks (GNNs) to solve a type of two-point nonlinear singular boundary value problems (TPN-SBVPs) that arise within thermal-explosion theory. The results of these investigation are provided for different neurons (4, 12 and 20), as well as absolute error along with the time complexity. For solving the TPN-SBVPs, a genetic algorithm (GA) and sequential quadratic programming (SQP) are used to optimize the error function. The accuracy of designed GNNs is provided by using a hybrid GA–SQP combination, which is based on a comparison of obtained and actual solutions. Furthermore, statistical analysis of the data is proposed in order to establish the competence as well as effectiveness of designed and the efficacy of the designed computing framework for solving the TPN-SBVPs.