2.3.12 Stencil diagrams: centering in time

**Figure 8:** Stencil diagrams with different time-centering: FTCS, time-centered implicit, BTCS, CTCS (leapfrog).
$\includegraphics[width=3.9cm]{images/pde1d_stencil_m0p.ps}$ $\includegraphics[width=3.9cm]{images/pde1d_stencil_CT-m0p.ps}$ $\includegraphics[width=3.9cm]{images/pde1d_stencil_BT-m0p.ps}$ $\includegraphics[width=3.9cm]{images/pde1d_stencil_leapfrog.ps}$

Figure 8 shows stencil diagrams for 4 schemes with CS and different time centering:

FT: forward-time (explicit)
time-centered implicit: (implicit)
BT: backward-time (fully implicit)
CT, Leapfrog: center-time (explicit, uses 3 time planes)

In implicit schemes each value at the new time level typically depends on all values at the old level: The full domain of dependence is larger than the direct domain of dependence.