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An additive finite-difference method for solving problems in laser thermochemistry. (English. Russian original) Zbl 1040.80503
Comput. Math. Math. Phys. 38, No. 9, 1514-1518 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 9, 1578-1582 (1998).
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. The scheme, which is implemented by means of an unconditionally stable diagonalization procedure, converges to a sufficiently smooth solution in the grid $$L_2$$-norm with an $$O(\tau+h^2)$$ error.
##### MSC:
 80M20 Finite difference methods applied to problems in thermodynamics and heat transfer 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 80A30 Chemical kinetics in thermodynamics and heat transfer