4.2. Domain of Dependence (DoD)

The domain of dependence is a measure of which grid points the numerical solution for a given grid point \(q_m^{n+1}\) depends on. If we, for example look at the FTBS scheme for the advection equation:

\[q_m^{n+1}=q_m^n-a\frac{\Delta t}{\Delta x}(q_m^n-q_{m-1}^n)\]

Here, the solution for \(q_m^{n+1}\) depends on the terms \(q_m^n\) and \(q_{m-1}^n\). We can annotate these dependencies in the discrete time-space domain:

Fig. 4.1 The Domain of Dependence (DoD), for the FTBS scheme to the linear advection equation.