In this article, a pair of hybrid block techniques is constructed and successfully applied to integrate Emden–Fowler third-order singular boundary problems. One of the proposed one-step hybrid block techniques is obtained by considering two intermediate points. The obtained method is then paired with a hybrid block strategy of order three to bypass the singularity at the left endpoint of the integration interval. Some third-order Emden–Fowler type problems are solved numerically to show the effectiveness of the proposed technique. The numerical results are compared with other recent numerical approaches in the literature, and the numerical simulations confirm the superiority and robust performance of the proposed strategy.

在本文中，构建了一对混合块技术并成功应用于集成 Emden-Fowler 三阶奇异边界问题。通过考虑两个中间点获得所提出的一步混合块技术之一。然后将获得的方法与三阶混合块策略配对，以绕过积分区间左端点处的奇点。一些三阶 Emden-Fowler 类型的问题被数值解决以显示所提出技术的有效性。数值结果与文献中其他最近的数值方法进行了比较，数值模拟证实了所提出策略的优越性和鲁棒性。