As with the heat equation we need sources for wavefields.
I prepared a
subroutine for stepping forward
the *HVP* operator while adding in sources
and used it for the dot-product test.
I find the test *y*'(*Ax*)=(*A*'*y*)'*x*
using random numbers for *x* and *y*
leads to the expected six digits of numerical accuracy
in a 100^{3} test.

I am not showing the wave stepping subroutine here because
it is just like `heatsteps()` but with minor added complications.

11/12/1997