The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination of the shooting method with a modification of the renowned Adomian decomposition method. The approach starts by transforming the governing BVP into two appropriate initial-value problems, and thereafter, solves the resulting IVPs recurrently. In addition, the application of this method to varied test models remains feasible—of course, this is supported by the competing Runge–Kutta method, among others, and reported through comparison plots and tables.

This research aims to present an efficient numerical method to find approximate numerical solutions for ordinary differential equations (ODEs), specifically, the class of two-point boundary value models. This approach is predicated on coupling the shooting method and the decomposition method, which the method is named as Efficient Decomposition Shooting Method (EDSM). Thus, we provide the complete outline of EDSM, and thereafter, apply it to some test models, comprising linear and nonlinear models. Further, the results are then validated by comparing them to the exact solution and other computational methods. Thus, the proposed method performs excellently over its peers, and is found to converge rapidly to the available exact solution with a good precision.