In the present investigation, a novel neuro-swarming intelligence-based numerical computing solver is developed for solving second order non-linear singular periodic (NSP) boundary value problems (BVPs), i.e., NSP-BVPs, using the modeling strength of artificial neural networks (ANN) optimized with global search efficacy of particle swarm optimization (PSO) supported with the methodology of rapid local search by interior-point scheme (IPS), i.e., ANN-PSO-IPS. In order to check the proficiency, robustness, and stability of the designed ANN-PSO-IPS, two numerical problems of the NSP-BVPs have been presented for different numbers of neurons. The outcomes of the proposed ANN-PSO-IPS are compared with the available exact solutions to establish the worth of the solver in terms of accuracy and convergence, which is further endorsed through results of statistical performance metrics based on multiple implementations.