Abstract —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.

中文翻译：

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基于解解析性的理想磁流体动力学问题时间积分数值算法

摘要 —我们表明，如果初始流速和磁场是空间的解析函数，理想磁流体动力学的三维方程组的解在具有严格正长度的某个时间间隔上的空间和时间变量中是解析的。变量。利用磁场的冻结特性，我们在欧拉坐标和拉格朗日坐标中构造解的时间泰勒展开式。我们推导出这些展开系数的递推关系，并将它们用于开发欧拉和拉格朗日算法，用于理想磁流体动力学方程的数值时间积分。Largangian 算法已经过计算测试；在溶液中观察到较小尺寸结构的形成。