  We propose a new method for Monte Carlo solution of non-linear integral
equations by combining the Newton-Kantorovich method for solving non-linear
equations with the Markov Chain Monte Carlo (MCMC) method for solving linear
equations. The Newton-Kantorovich method allows to express the non-linear
equation as a system of the linear equations which then can be treated by the
MCMC (random walk) algorithm. We apply this method to the Balitsky-Kovchegov
(BK) equation describing evolution of gluon density at low x. Results of
numerical computations show that the MCMC method is both precise and efficient.
The presented algorithm may be particularly suited for solving more complicated
and higher-dimensional non-linear integral equation, for which traditional
methods become unfeasible.
