4.1 Review of cases used

For the Fortran implementation, the following methods are implemented. The explicit FTCS, Explicit Lax, Implicit FTCS, and Implicit Crank-Nicolson.

For each method, the following was generated

1. CPU time used for the run.
2. snap shot of the solution at \(t=0,t=15,\) and \(t=30\) minutes.
3. RMSE between the numerical solution and the analytical solution.
4. Animation of the numerical solution. The animation was done by taking snapshots of the solution at regular intervals in Fortran. These were saved to disk. Then Mathematica was used to generate the animation and the plots.

To compare the stability and accuracy of the methods, the time step was changed (increased) and a new run was made. 8 different values of time steps are used. So there are 8 tests cases. These 8 test cases were run for both fixed speed \(\left ( u=2\text { ft/min}\right ) \) and for \(u=\frac {t}{20}\) ft/min.

This table below summarizes these cases.  The appendix contains all the plots. The animations are added as HTML links.