2.4.4 BTCS scheme

Figure 10: BTCS scheme: stencil diagram and test result.

Figure 10 shows the stencil diagram and an example for the fully implicit BTCS scheme with flux at $i+\frac{1}{2}$

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ f \! ... ...ht) + f \! \left( \rho_{i}^{n+1} \right) \right] \enspace .$$ (107)