This paper shows new approximate ways to solve nonlinear ordinary differential equations using two methods that repeat steps: the Adomian decomposition method (ADM) and the optimal Adomian decomposition method (OADM). These equations are extensively utilized in fluid dynamics and engineering. The OADM sets itself apart by incorporating an optimal control parameter that enhances solution accuracy and accelerates convergence, providing a distinct advantage over the ADM. The two methods have been applied to three important equations: the Darcy-Brinkmann-Forchheimer moment equation, the Blasius equation, and the Falkner-Skan equation. The effectiveness of the two methods was assessed by looking at how quickly they converged and the largest error remaining, while also comparing them to other numerical results from operational matrix methods found in existing research. The results demonstrate the superior accuracy of OADM, which proves its effectiveness in solving the nonlinear equations. All computations were conducted utilizing the program, which facilitated the execution and evaluation of the proposed methods
Al-Zubaidi et al. (Thu,) studied this question.