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Variable coefficients (1)
3D wave equation:
\varrho u_{tt} = (qu_x)_x + (qu_y)_y + (qu_z)_z + f(x,y,z,t)
Just apply the 1D discretization for each term:
\begin{equation}
[\varrho D_tD_t u = (D_x\overline{q}^x D_x u +
D_y\overline{q}^y D_yu + D_z\overline{q}^z D_z u) + f]^n_{i,j,k}
\end{equation}
Need special formula for u^1_{i,j,k}
(use [D_{2t}u=V]^0 and stencil for n=0 ).
