Runge-Kutta methods and viscous wave equations

We study the numerical time integration of a class of viscous wave equations by means of Runge-Kutta methods. The viscous wave equation is an extension of the standard second-order wave equation including advection-diffusion terms differentiated in time. The viscous wave equation can be very stiff so that for time integration traditional explicit methods are no longer efficient. A-stable Runge-Kutta methods are then very good candidates for time integration, in particular diagonally implicit ones