Estimates of the Convergence of Iterative Methods for Numerical Simulation of 3D Processes in Magnetohydrodynamics

Convergence of iterative processes applied to implicit completely conservative difference schemes of three-dimensional magnetohydrodynamics in the framework of methods of separate and combined solution of groups of difference equations that are split by physical processes is studied. Estimates of the convergence of iterative processes for the numerical methods considered in this work are obtained. The scope of both the combined and separate methods for solving the 3D difference equations of magnetohydrodynamics is investigated. Taking into account the fact that the study of the presented algorithms is mainly of a qualitative nature, the validity of the obtained estimates is confirmed by numerical experiments, and both model and real problems are considered. Note that the obtained estimates of convergence of the iterative processes make it possible to choose the optimal numerical method for solving difference equations of 3D magnetohydrodynamics at any time step.