F-transform; Higher Degree F-transform; Shooting method; Differential equation;

We study the framework of the shooting methodfor nonlinear second-order ordinary differential equations with boundary conditions. We propose a new numerical scheme, based on the second degree F-transform for solving the corresponding initial value problem. Moreover, we use the inverse F-transforms of the zero and first degrees to extend the numerical solution to the initial domain. We make experiments that demonstrate the effectiveness of the proposed F-transform-based shooting method in the class of second order numerical methods.