An additive finite-difference method for solving problems in laser thermochemistry

A new approach to the construction of conservative monotone difference schemes is proposed for the system of equations of laser thermochemistry with well-developed thermal diffusion. These equations are employed in the classical drift-diffusion model of chemical kinetics. Based on the approach proposed, a conservative finite-difference scheme is constructed for these equations, which retains the sign of nonnegative solutions. The scheme, which is implemented by means of unconditionally stable diagonalization procedures, converges to a sufficiently smooth solution in the grid L 2 -norm with an O(τ + h 2 ) error.