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.

本研究的目的是通过基于人工神经网络（ANN）数学建模的神经群智能计算求解器ANN–PSO–SQP的开发，解决奇异的二阶泛函微分模型。优化（PSO）有助于顺序二次规划（SQP）的本地搜索效率。在方案ANN-PSO-SQP中，基于误差的目标函数借助于ANN的连续映射用于二阶奇异函数差分模型，并通过PSO与SQP的组合强度进行了优化。ANN-PSO-SQP设计的灵感来自于提出一个精确，可靠和可行的框架，以处理涉及延迟，受电弓和预测项的刚性奇异功能模型。针对奇异的二阶功能差分模型的三种不同变体，对设计的方案进行了测试。将所提议的ANN–PSO–SQP的单次或多次运行所获得的结果与确切的解决方案进行比较，以验证功效，正确性和可行性。