Shooting method based on higher degree F-transform

We study the framework of the shooting method for 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. We use the inverse F-transforms of the zero and first degrees to obtain approximate solutions to the initial second-order differential equation. We make experiments that demonstrate effectiveness of the proposed F-transform-based shooting method in the class of second order numerical methods.