An efficient numerical algorithm for simulating a two-dimensional glow discharge

A numerical algorithm of the second approximation order with respect to the space variables for simulating a two-dimensional elevated pressure glow discharge in the framework of the drift-diffusion approximation is presented. A specific feature of this algorithm is the use of the Laplace resolving operator for the solution of the system of grid equations. This makes it possible to ensure the convergence of the solution in strong grid norms. Mathematical aspects of the statement of the differential-difference and finite difference problems (solvability, nonnegativity, approximation, stability, and convergence) are discussed, and bounds on the norms of the corresponding differential and difference operators that are required for constructing an optimal iterative process are obtained.