2.4.3 Implicit centered scheme

Figure 10: Implicit centered scheme: stencil diagram and test result.

Figure 10: Implicit centered scheme with flux

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{4} \left[ f \! ... ...ht) + f \! \left( \rho_{i}^{n+1} \right) \right] \enspace .$$ (111)

The centering of the scheme in space and time seemed promising. However, the initial condition is severely distorted.