Sean,

you can visualize data of type {{t0, x0}, {t1, x1}, {t2, x2}, ...} with ListPlot, see

http://reference.wolfram.com/mathematica/ref/ListPlot.html

The function or interpolation function you would get from Nick's suggestion can be visualized with Plot:

http://reference.wolfram.com/mathematica/ref/Plot.html

If you are not required to use any particular numerical method then I would also strongly recommend you to use either DSolve or NDSolve to find your answer. Hope this helps.

Hello Sean,

I am not that good at physics, so I apologies if my idea does to fit to the purpose. 

I would suggest loosing the "For" loop. It is my experience with Mathematica, that whenever you use loops, there is a more clean way of doing things. In your case, I might consider using Recurrence Table, and then merge the lists using Transpose. Then you can plot the data via ListPlot. :-)

For instance:
Hope it helps, or that someone can help you with a better answer :-)

Edit: As I am sure you recognized, I left out writing the "V[n+1]". Simply because I fear I would write the expression wrong when I do not know the physics behind it in detail. So it is for you to fill out :-)

Edit 2: I completely forgot to say that RecurrenceTable allows for more systems of equations than just a single one. In which case you will not need to Transpose prior plotting, I presume. Check out http://reference.wolfram.com/mathematica/ref/RecurrenceTable.html.