Neuro-swarm intelligent computing to solve the second-order singular functional differential model

The aim of the present study is to solve the singular second-order functional differential model with the development of neuro-swarm intelligent computing solver ANN–PSO–SQP based on mathematical modeling of artificial neural networks (ANNs) optimized globally search efficacy of particle swarm optimization (PSO) aided with local search efficiency of sequential quadratic programming (SQP). In the scheme ANN–PSO–SQP, an error-based objective function is assembled with the help of continuous mapping of ANN for second-order singular functional differential model and optimized with combination strength of PSO with SQP. The inspiration for the design of ANN–PSO–SQP comes with an objective to present a precise, reliable and feasible frameworks to handle with stiff singular functional models involving the delayed, pantograph and prediction terms. The designed scheme is tested for three different variants of the singular second-order functional differential models. The obtained outcomes on both single as well as multiple runs of the proposed ANN–PSO–SQP are compared with the exact solutions to validate the efficacy, correctness and viability.