The method of continuous continuation by a parameter for solving boundary-value problems for nonlinear systems of differential-algebraic equations with delay that have singular points

In this paper, we consider a numerical method for solving a nonlinear boundary-value problem for a system of differential-algebraic equations with a delayed argument that have singular limit points. For a numerical solution of the boundary-value problem, the shooting method is used. The value of the shooting parameter is calculated by the Newton method. We consider the case where the problem is ill-posed and hence the method may diverge. In this case, the solution is constructed by the method of the best parameter, namely, the length of the curve of the set of solutions. The solution of the initial problem for each value of the shooting parameter is calculated using the method of continuous continuation by the best parameter.