In this paper a theoretical model is presented for the physicochemical processes in gas medium around a carbon particle heated by intense laser radiation in a humid air under condition of low concentration of oxygen near its surface. In this case, as it was shown previously, the zone of homogeneous burning of hydrogen - a product of reaction between carbon and water vapor - is moving away from the particle surface. The solving of a boundary problem for three differential equations of second order was obtained by a finite difference method. The results are compared with those obtained previously for the same problem parameters when another method was applied.