Design of neuro-evolutionary model for solving nonlinear singularly perturbed boundary value problems

In this study, a neuro-evolutionary technique is developed for solving singularly perturbed boundary value problems (SP-BVPs) of linear and nonlinear ordinary differential equations (ODEs) by exploiting the strength of feed-forward artificial neural networks (ANNs), genetic algorithms (GAs) and sequential quadratic programming (SQP) technique. Mathematical modeling of SP-BVPs is constructed by using a universal function approximation capability of ANNs in mean square sense. Training of design parameter of ANNs is carried out by GAs, which is used as a tool for effective global search method integrated with SQP algorithm for rapid local convergence. The performance of the proposed design scheme is tested for six linear and nonlinear BVPs of singularly perturbed systems. Comprehensive numerical simulation studies are conducted to validate the effectiveness of the proposed scheme in terms of accuracy, robustness and convergence.