Revised and enhanced analysis of a recent novel iterative algorithm

In this study, we rectify the recent results related to the stability of a novel iterative algorithm proposed by [P. Sharma, H. Ramos, R. Behl, V. Kanwar, J. Comput. Appl. Math., \( \bf 430\) (2023), 15 pages] using a broader concept of stability, known as weak \(w^2\)-stability. Additionally, to prove the resilience of this iteration, we establish new results regarding data dependency and weak convergence. We provide non-trivial examples to highlight the accuracy of our theoretical findings. Moreover, we demonstrated that the aforementioned iterative algorithm serves as a potential technique for solving a specific delay differential equation.