Design of Mexican Hat Wavelet neural networks for solving Bratu type nonlinear systems

In this paper a Mexican Hat Wavelet based neural network is designed and applied for solving the nonlinear Bratu type equation. This equation is widely used in fuel ignition models, electrically conducting solids and heat transfer studies. The Mexican Hat Wavelet Differential equation artificial neural networks (MHW-DEANN) are used for the first time to construct an energy function of the system in an unsupervised manner. The tunable parameters of MHW-DEANN are trained with a hybrid evolutionary computing approach: we exploit the strength of Genetic Algorithms (GA) and Sequential Quadratic Programming (SQP) to find the best weights. Monte-Carlo simulations are performed for the proposed scheme with statistical analysis to validate the effectiveness and convergence of the proposed method for Bratu-type equations. It is observed that the proposed method converges in all cases and can solve the equation with high accuracy and reliability.