On the parametrization of numerical solutions to boundary value problems for nonlinear differential equations

Certain techniques are proposed for improving the computational process of integrating boundary value problems for systems of nonlinear ordinary differential equations (ODEs) with nonlinear boundary conditions. These techniques are based on the shooting method and the continuation method, including the continuation with respect to the optimal parameter. The proposed approach makes it possible to significantly expand the class of problems that can be numerically solved by the shooting method.