A Numerical Algorithm for Time Integration of the Problems of Ideal Magnetohydrodynamics Based on Analyticity of Their Solutions

—We show that a solution of the system of three-dimensional equations of ideal magnetohydrodynamics is analytic in the spatial and temporal variables on a certain time interval with a strictly positive length provided that the initial flow velocity and magnetic field are analytic functions of spatial variables. Utilizing the property of frozenness of the magnetic field, we construct time Taylor expansions of the solution in the Eulerian and Lagrangian coordinates. We derive recurrence relations for the coefficients of these expansions and employ them for developing the Eulerian and Lagrangian algorithms for numerical time integration of the equations of ideal magnetohydrodynamics. The Largangian algorithm has been tested in computations; the formation of the structures of a smaller dimension is observed in the solution.