# The problem definition in G. Sadaka's Wave Equation example

G. Sadaka provide an examplein solving Wave Equation. Math equation is:

The problem definition in Sadaka’s code is:

``````problem tambour(uh,vh) = int2d(Th)(uh*vh + Grad(uh)'*Grad(vh)*(c*dt)^2*.5 )
I want to know why there is a `int2d(Th)(Grad(uh0)'*Grad(vh)*(c*dt)^2*.5 ) ` term (the 2nd row). If we approximate `u_tt` with `(u-2*u_{t-1}+u_{t-2})/(dt)^2` and set `u_{t-1}` to `uh1`, `u_{t-2}` to `uh0`, then we can get the 1st and 3rd row but not the 2nd.
Finally I find that Sadaka use `(\Delta u+\Delta u_{t-1})/2` to approximate `\Delta u`，so there is a `.5` in the problem.