Neuron Analysis of the Two-Point Singular Boundary Value Problems Arising in the Thermal Explosion's Theory

The purpose of the present study is to present the neuron analysis using the unsupervised artificial neural networks (US-ANNs) for solving a class of two-point nonlinear singular boundary value problems (TPN-SBVPs) arising in the thermal explosion's theory. The analysis using small and large neurons (3, 10 and 30 neurons) is presented along with the absolute error performances and complexity cost. An error function is optimized using the global and local search mechanisms called genetic algorithm (GA) and active-set approach (ASA) for solving the TPN-SBVPs. The correctness of the designed scheme US-ANNs using the hybrid combination of GA-ASA is approved through the comparison of obtained and true solutions. Moreover, statistical analysis will also be performed to authenticate the reliability and competency of the proposed method for solving the singular model.

Automated summary

The present study aims to solve a class of nonlinear boundary value problems arising in the thermal explosion's theory using unsupervised artificial neural networks. The analysis includes different numbers of neurons, absolute error performances, and complexity cost. Genetic algorithm and active-set approach are used to optimize the error function for solving the problems. The designed scheme using the hybrid combination of GA-ASA is validated by comparing the obtained solutions with the true solutions. Additionally, statistical analysis is performed to verify the reliability and competency of the proposed method for solving the singular model.