Improved shooting method for solving a boundary value problem with a power-law nonlinearity

Abstract

This work investigates a class of nonlinear second-order boundary value problems with a power-type nonlinearity. To solve such problems, an improved shooting method is proposed that combines the classical shooting approach with a numerical–analytical technique based on power series expansions and analytic continuation. The method allows one to control the domain of analyticity of the solution and to obtain a priori error estimates at each continuation step. Numerical experiments are presented to demonstrate the effectiveness and accuracy of the proposed approach. A comparative analysis with the classical numerical shooting method based on Runge–Kutta integration is also provided.