Artificial hybrid neural network-based simultaneous scheme for solving nonlinear equations: Applications in engineering

A novel three-step simultaneous scheme for finding all distinct and multiple roots of non-linear equations are developed in this paper. Analysis of convergence demonstrates that the newly created scheme has an order of convergence of eight. A hybrid neural network-based simultaneous technique is also developed to expedite convergence. Neural network-based approaches outperform existing methods in terms of iterations, error, and CPU time, as demonstrated by the engineering applications’ results. The analysis of the considered approaches on random starting approximations reveals that the newly proposed methods are more stable and consistent than previous methods.