I am trying to understand the stability of a finite difference equation on the staggered grid.
I could understand the Von Neumann stability analysis for the collocated grid for a simple acoustic equation as explained in this tutorial and in this Von Newman stability analysis for 2D acoustic wave equation explicit.
However the problem is to analyse the wave equation which is presented in coupled form on staggered grid such as :
Above equations are better shown as in appendix A of following
Any suggestions for stability analysis of this kind pde problems?