Finite Difference Implementation

For my numerical methods course–a course centered around the tools and techniques used in modeling ocean systems–we have been tasked with programing a 1D model of a differential equation with simple initial conditions. Our implementation has to be in Fortran, a computer language with a long history, which has been a bit of a learning curve to say the least.
Nevertheless, I wanted to take couple minutes and share my preliminary results here.

Update:

You can checkout my full article with results here or checkout the source code and results here.