Derivative-free method for singular systems

This paper presents algorithm for solving singular nonlinear system. Since the convergence rate of any method to singular solution drops down, the convergence can be accelerated by forming the bordered system. Singular vectors of the Jacobian can be used for the construction of the bordered system. The Jacobian is usually unavailable, so singular vectors of the finite difference approximation of the Jacobian are used in forming the bordered system and local algorithm for solving it is presented. Algorithm is tested on two numerical examples.