A Modification of the Efficient Decomposition Shooting Method for Two-Point Boundary-Value Problems

This research aims to present two modified numerical approaches based on the efficient decomposition shooting method (EDSM) to find approximate and reliable solutions to the class of ordinary differential equations (ODEs), featuring the two-point boundary-value problems (BVPs). In fact, the two famous modifications of the Adomian decomposition method (ADM) are sought and further infused in the classical shooting method to unravel the two schemes of interest. Further, the proposed schemes are applied to several second and third-order BVPs of both the linear and nonlinear cases. Moreover, the proposed schemes perfumed superbly in comparison with some contending approaches in the literature. What is more, the convergence rate of the devised schemes is found to be very high.