Steady state solution of warped accretion discs

We consider a thin accretion disc warped due to the Bardeen-Petterson effect, presenting both analytical and numerical solutions for the situation that the two viscosity coefficients vary with radius as power law, with the two power law indices not necessarily equal. The analytical solutions are compared with numerical ones, showing that our new analytical solution is more accurate than previous one, which overestimates the inclination changing in the outer disc. Our new analytical solution is appropriate for moderately warped discs, while for extremely misaligned disc, only numerical solution is appropriate.