Stability analysis for a hyperbolic PDE on staggered grid

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?

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asked Jul 22 '16 at 15:56

Amartya

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$\begingroup$ Usually stability analysis or error analysis is done for the most simplified forms of the equations. This is so because as the equations become more complicated, analysis becomes intractable. In the link, the equation is transformed to a first order hyperbolic system. I guess your best bet would be to simplify it as much as possible, say making it into 1D. Maybe that will make it tractable. $\endgroup$ – Vikram Jul 25 '16 at 8:41
$\begingroup$ I agree with your suggestion about simplifying the equation to 1D form. The link was provided to give an idea about the equation I am dealing with. I read this post scicomp.stackexchange.com/questions/7156/… which gives very good idea how to handle higher order. Now I have only two concerns- coupled form and staggered gird (as highlighted in my questions) since field variables (stress and velocity) are defined at different locations. $\endgroup$ – Amartya Jul 26 '16 at 11:47

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