CONVERGENCE ESTIMATES OF ITERATIVE METHODS FOR NUMERICAL MODELING OF THREE-DIMENSIONAL PROCESSES IN MAGNETOHYDRODYNAMICS

This paper addresses the convergence of iterative processes applied to implicit, fully conservative difference schemes in three-dimensional magnetohydrodynamics, using both separate and combined solution methods for groups of difference equations split by physical processes. Convergence estimates for the iterative processes of the numerical methods considered in this study are obtained. The applicability of both combined and separate methods for solving three-dimensional difference equations in magnetohydrodynamics is examined. Given that the presented algorithm analysis is mainly qualitative, the validity of the obtained estimates was confirmed through numerical experiments on both model and real-world problems. Notably, the convergence estimates of the iterative processes allow for the selection of an optimal numerical method for solving difference equations in three-dimensional magnetohydrodynamic problems at any time step.