A design of novel Gudermannian neural networks for the nonlinear multi-pantograph delay differential singular model

Abstract

Abstract In this paper, a new stochastic numerical platform through the Gudermannian neural network (GNN) based intelligent computing solver (GNNICS) is accessible for solving the nonlinear singular multi-pantograph delay differential (MP-DD) systems. In GNNICS, Gudermannian kernel is exploited to construct the neural network models of differential operators with different neurons for the nonlinear system along with the hybrid computing via global genetic algorithm (GA) and local refinements based active set (AS), i.e., GNN-GAAS method. A fitness function with GNN models is formulated for solving the MP-DD equation along with the optimization of design variables of the network using GAAS. To investigate the performance of the designed GNNICS based GNN-GAAS algorithm, three different variants of the MP-DD systems are used to assess the correctness, effectiveness, and robustness. The statistical investigations based on different performance are presented to authenticate the consistent accuracy, convergence, and stability of the designed GNN-GAAS algorithm. Furthermore, the negligible absolute error that are performed as 10−06 to 10−08 for solving the GNNICS based on GNN-GAAS algorithm.