The errors of analytical results come from the approximation of the theoretical model and the improper presentation of the physical environments and procedures. When a simulation model comes from a theoretical model, it also has errors generated by the analytical results. In addition, a numerical method has its own errors during the simulation process due to computation accuracy and imperfect representation of those continuous processes, such as differentiations in time and space. Simple error analysis can be conducted on the basis of each of the simulation equations, as shown in the error terms of eq.(49)-(54). Further error analysis of the whole system becomes much more prohibitive because of the complexity of the MHD equations. The comparison of simulation results with analytical results for simple problems can give us some very useful ideas of the errors of the MHD equation system.
Here we will discuss two important errors arising from MHD simulations: diffusion error and fluctuation error. A more complete analysis can be found in the publications listed in section 7.