Analytical solution for magnetized thin accretion disk in comparison with numerical simulations

We obtained equations for a thin magnetic accretion disk, using the method of asymptotic approximation. They cannot be solved analytically-without solutions for a magnetic field in the magnetosphere between the star and the disk, only a set of general conditions on the solutions can be derived. To compare the analytical results with numerical solutions, we find expressions for physical quantities in the disk, using our results from resistive and viscous star-disk magnetospheric interaction simulations.