I am calculating the temperature of a rod which has one end at the temperature T1 and the other end at T2 and it's evolution. We were already given the formula for the numeric calculation and after a short while I managed to obtain a small program that would calculate the temperature of each segment of the T(x,t) grid:
>restart: with(plots): nx:=20: tmax:=50: T1:=1: T2:=10: L:=1: k:=1: rho:=1: cp:=1: chi:=k/rho/cp: h:=L/(nx-1): t:=1e-3:
>for k from 0 to nx do T(k,0):=T1 od:
for w from 1 to tmax do
for q from 1 to nx-1 do
With L the Length of the rod, t and h the time and space increment [h=L/(nx-1), where nx is the number of intervals we divide the x-axis, although I'm not quite sure the '-1' should be there], chi a constant different for each rod and tmax total time we want to calculate. The formula from the 5th line was given to us, so in that part there is no mistake.
Up until here everything works perfectly fine.
Now I want to be able to draw this and here is where all the problems appear. I want to draw this in a 2D graph with position in the x-axis and time in the y-axis. I have tried "densityplot(T(x,y),x=0..nx,y=0..tmax)" which would seem to be the logical whay to continue this. As I understand it, this plot would draw an nx times tmax grid and colour the whole plpot black-white acording to the maximum and the minimum value (as shown in the maple help page of this plot).
However, when I do this a black square appears (or red if I add colorstyle=HUE). I have tried a lot of things and none seemed to work.
I would also like to be able to draw the isotherms on the plot but that is secondary.
I am pretty new to Maple. I have studied the most basic things but don't really understand the whole complexity of this program. Thanks a lot in advance and forgive my faulty english,