Lie Group Solution Of Two - Dimensional Magnetohydrodynamics Equations And The Probability Of Solutions

In recent years, magnetohydrodynamics(MHD) equations has been more and more get the attention of scholars. Lots of mathematics are dedicated to the MHD equations and the numerical solutions. Based on classical Lie Group method, we study 2D ideal incompressible MHD equation and get its infinitesimal generator. Then through a known solution, we can obtain other more solutions. Taking advantage of these exact solutions we study the stability and uniqueness of initial-boundary problem on MHD.In this paper, we establish the finite difference scheme of the two-dimensional MHD equations for the initial-boundary value problem and analyzes truncation error and convergence of the difference scheme. Finally, we simulate the difference and compare with the exact solution by Matlab software. Verify the theoretical results.