We present a Finite-Volume scheme for solving the equations of radiation magnetohydrodynamics. This system is for example used to model the plasma in the solar convection zone and in the solar photosphere. The starting point is a basic scheme for conservation laws. We first study the convergence of the scheme applied to a model problem for the full system of radiation magnetohydrodynamics. We then present modifications of the base scheme which make it possible to approximate the system with an arbitrary equation of state, reduce errors due to a violation of the divergence constraint on the magnetic field, and lead to an improved accuracy in the approximation of solution near an equilibrium state. These modifications are essential for an accurate simulation of processes in the solar atmosphere. For simulations in the solar photosphere, we additionally have to take the radiation intensity into account. A scheme for solving the radiation transport equation is thus a further focus of this study.

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