2.4.4 BTCS scheme

Figure 11: BTCS scheme: stencil diagram and test result.

Figure 11: fully implicit BTCS scheme with flux

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ f \! ... ...ht) + f \! \left( \rho_{i}^{n+1} \right) \right] \enspace .$$ (112)

The fully implicit treatment takes effect: the result looks almost smooth (with some non-decaying small-scale wiggles) but is smeared out heavily.