Parametrization of the numeric solution of nonlinear boundary value problems

Some approach for numerical solution of boundary value problem (BVP) for system of nonlinear ordinary differential equations with nonlinear boundary conditions is proposed. The main idea of the methods consists in various combinations the shooting method and the continuation method with respect to a parameter, including the arclength. Such methods improve the standard methods of solving BVP and expand the class solvable problems. An example is considered.