[en] The paper presents the mathematical model of combustion initiation in a mixture of hydrogen and oxygen gases (oxyhydrogen) by a laser flare created near a metal barrier. For numerical resolution of the ‘hyperbolic’ part of Reynold’s equations system, we give a new nonlinear quasimonotone compact polynomial difference scheme of improved accuracy. Calculations of all the main parameters: the laser flare, the heating of the metal barrier, and the combustion processes in the hydrogen–oxygen system are performed. (paper)