In this paper, a novel meta-heuristic computing solver is presented for solving the singular three-point second-order boundary value problems using artificial neural networks (ANNs) optimized by the combined strength of global and local search ability of genetic algorithms (GAs) and interior point algorithm (IPA), i.e., ANN–GA–IPA. The inspiration for presenting this numerical work comes from the intention of introducing a consistent framework that combines the effective features of neural networks optimized with the contexts of soft computing to handle with such challenging systems. Three numerical variants of singular second-order system have been taken to examine the proficiency, robustness, and stability of the designed approach. The comparison of the proposed results of ANN–GA–IPA from available exact solutions shows the good agreement with 5 to 7 decimal places of the accuracy which established worth of the methodology through performance analyses on a single and multiple executions.

本文提出了一种新颖的元启发式计算求解器，该算法使用人工神经网络（ANN）来解决奇异的三点二阶边值问题，而人工神经网络是通过遗传算法（GA）的全局和局部搜索能力的组合而优化的和内部点算法（IPA），即ANN–GA–IPA。提出此数值研究的灵感来自于引入一个一致的框架的意图，该框架结合了经过优化的神经网络的有效功能以及软计算的上下文，以应对此类具有挑战性的系统。奇异二阶系统的三个数值变体已被采用来检验设计方法的熟练程度，鲁棒性和稳定性。