F-transform-based shooting method for nonlinear boundary value problems

Abstract

We study a class of ordinary two-point boundary value problems for nonlinear second-order ordinary differential equations. We propose to use the framework of shooting method and apply the second-degree F-transform for solving the corresponding initial value problem. We make experiments that demonstrate effectiveness of the proposed F-transform-based shooting method in the class of second-order numerical methods. Moreover, we show stability of the proposed method and its ability to "ignore noise".