Dynamics of three-point boundary value problems with Gudermannian neural networks

The present study articulates a novel heuristic computing design with artificial intelligence algorithm by manipulating the models with Feed forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of Genetic algorithms (GA) combined with rapid local convergence of Active-set method (ASM), i.e., FF-GNN-GAASM for solving the second kind of Three-point singular boundary value problems (TPS-BVPs). The proposed FF-GNN-GAASM intelligent computing solver integrated into the hidden layer structure of FF-GNN systems of differential operatives of the second kind of STP-BVPs, which are linked to form the error based Merit function (MF). The MF is optimized with the hybrid-combined heuristics of GAASM. The stimulation for presenting this research work comes from the objective to introduce a reliable framework that associates the operational features of NNs to challenge with such inspiring models. Three different measures of the second kind of TPS-BVPs is applied to assess the robustness, correctness and usefulness of the designed FF-GNN-GAASM. Statistical evaluations through the performance of FF-GNN-GAASM is validated via consistent stability, accuracy and convergence.

Automated summary

The present study introduces a novel heuristic computing design for solving the second kind of Three-point singular boundary value problems (TPS-BVPs) by combining Feed forward Gudermannian neural networks (GNN) with Genetic algorithms (GA) and Active-set method (ASM). The proposed intelligent computing solver, FF-GNN-GAASM, is integrated into the hidden layer structure of FF-GNN systems, optimizing the error based Merit function (MF) with the hybrid-combined heuristics of GAASM. The performance of FF-GNN-GAASM is evaluated through statistical assessments, demonstrating consistent stability, accuracy, and convergence.