Convergence estimates of some iterative algorithms for numerical modeling of two-dimensional equations of magnetohydrodynamics

In this work, the convergence of the methods of separate and combined solution of difference equations groups separated by physical processes, applied to completely conservative difference schemes (CCDS) of two-dimensional magnetohydrodynamics, is studied. The corresponding estimates for the convergence of iterative processes for the entire family of CCDS are obtained. The area of applicability of this method is shown. The validity of the estimates obtained in the work is confirmed by numerical calculations. Depending on the velocity of convergence of the iterative process, based on the estimates determined in this work, recommendations were developed on the use of one of the two methods under study (separate or combined solution of groups of difference equations).