  The systems of nonlinear Volterra integral equations of the first kind with
jump discontinuous kernels are studied. The iterative numerical method for such
nonlinear systems is proposed. Proposed method employs the modified
Newton-Kantorovich iterative process for the integral operators linearization.
On each step of the iterative process the linear system of integral equations
is obtained and resolved using the discontinuity driven piecewise constant
approximation of the exact solution. The convergence theorem is proved. The
polynomial collocation technique is also applied to solve such systems as the
alternative method. The accuracy of proposed numerical methods is discussed.
The model examples are examined in order to demonstrate the efficiency of
proposed numerical methods and illustrate the constructed theory.
