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The author of the method was Anatoly V. Draghilev.

         We represent a method of a numerical solution of systems of the nonlinear equations.
       This method is original. It is beening developed during many years in a form of
private initiative. The programs realizing algorithm of this method, were tested on many
examples. For instance, our method was  useful  in solving such problems as a
determination of the roots of a system of the ordinary nonlinear differential equations
with boundary conditions (Duffing equation), and a construction of level lines F (x, y)= 0
and surfaces of level F (x, y, z) = 0.
         We consider a system of the nonlinear equations:
     
F( x ) = 0;

(1)
   

F=

 (
f1
...
fn
)
    
fi = fi( x1 , ... , xn ) ;
n
x Î E
   
         And fi has continuous partial derivatives of the 1-st order on xj (j = 1,..., n). x0 – start point;
F(x0) = F0. Let add n+1 independent variable t to (1).