Markov Chain Mote Carlo solution of BK equation through Newton-Kantorovich method
Abstract
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.
Keywords
Cite
@article{arxiv.1305.4154,
title = {Markov Chain Mote Carlo solution of BK equation through Newton-Kantorovich method},
author = {Krzysztof Bozek and Krzysztof Kutak and Wieslaw Placzek},
journal= {arXiv preprint arXiv:1305.4154},
year = {2015}
}
Comments
10 pages, 2 figures, typos corrected, accepted by JHEP