...
Therefore, in the numerical scheme I have made, I have defined the spacial resolution we are after, and the software computes a suitably small time step to be used. Making the time step and space step smaller is benefitial in reducing the numerical error, but (because my code is rather inefficiently written) will increase the computation time significantly. Worth trying to check though 
Location of current code: https://github.com/antiacids/RT-Sims
Notes from 16.90 on finite difference & FTCS: course/16/16.90/BackUp/www/pdfs/Chapter13.pdf
Results of the Simulation
...