$ octave --no-gui heatEquation2.m
Nx =  10
Nt =  5
dx =  0.10000
dt =  0.0050000
c =  1
xmin = 0
xmax =  1
tmin = 0
tmax =  1
r =  0.50000
rr =    2.2204e-16
Vectors x
ans =

   0.00000
   0.10000
   0.20000
   0.30000
   0.40000
   0.50000
   0.60000
   0.70000
   0.80000
   0.90000
   1.00000

Vector t
ans =

   0.000000
   0.005000
   0.010000
   0.015000
   0.020000
   0.025000

Result traspose(u)
ans =

 Columns 1 through 8:

   0.00000   0.30902   0.58779   0.80902   0.95106   1.00000   0.95106   0.80902
   0.00000   0.29389   0.55902   0.76942   0.90451   0.95106   0.90451   0.76942
   0.00000   0.27951   0.53166   0.73176   0.86024   0.90451   0.86024   0.73176
   0.00000   0.26583   0.50564   0.69595   0.81814   0.86024   0.81814   0.69595
   0.00000   0.25282   0.48089   0.66189   0.77809   0.81814   0.77809   0.66189
   0.00000   0.24044   0.45735   0.62949   0.74001   0.77809   0.74001   0.62949

 Columns 9 through 11:

   0.58779   0.30902   0.00000
   0.55902   0.29389   0.00000
   0.53166   0.27951   0.00000
   0.50564   0.26583   0.00000
   0.48089   0.25282   0.00000
   0.45735   0.24044   0.00000

Result u - Result of PDE explicit method.
u =

   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.30902   0.29389   0.27951   0.26583   0.25282   0.24044
   0.58779   0.55902   0.53166   0.50564   0.48089   0.45735
   0.80902   0.76942   0.73176   0.69595   0.66189   0.62949
   0.95106   0.90451   0.86024   0.81814   0.77809   0.74001
   1.00000   0.95106   0.90451   0.86024   0.81814   0.77809
   0.95106   0.90451   0.86024   0.81814   0.77809   0.74001
   0.80902   0.76942   0.73176   0.69595   0.66189   0.62949
   0.58779   0.55902   0.53166   0.50564   0.48089   0.45735
   0.30902   0.29389   0.27951   0.26583   0.25282   0.24044
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000

Result uu - Result of PDE anlytical solution u(x, t) = exp(-pi^2 * t) * sin(pi * x) method.
uu =

   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.30902   0.29414   0.27997   0.26649   0.25366   0.24145
   0.58779   0.55948   0.53254   0.50690   0.48249   0.45926
   0.80902   0.77006   0.73298   0.69769   0.66410   0.63212
   0.95106   0.90526   0.86167   0.82018   0.78069   0.74310
   1.00000   0.95185   0.90602   0.86239   0.82087   0.78134
   0.95106   0.90526   0.86167   0.82018   0.78069   0.74310
   0.80902   0.77006   0.73298   0.69769   0.66410   0.63212
   0.58779   0.55948   0.53254   0.50690   0.48249   0.45926
   0.30902   0.29414   0.27997   0.26649   0.25366   0.24145
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000

Error between analytical solution and computed PDE explicit metod solution
ans =

   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000
   0.0000000   0.0002451   0.0004665   0.0006657   0.0008446   0.0010045
   0.0000000   0.0004663   0.0008873   0.0012663   0.0016065   0.0019106
   0.0000000   0.0006418   0.0012213   0.0017430   0.0022111   0.0026297
   0.0000000   0.0007545   0.0014357   0.0020490   0.0025993   0.0030914
   0.0000000   0.0007933   0.0015096   0.0021544   0.0027331   0.0032505
   0.0000000   0.0007545   0.0014357   0.0020490   0.0025993   0.0030914
   0.0000000   0.0006418   0.0012213   0.0017430   0.0022111   0.0026297
   0.0000000   0.0004663   0.0008873   0.0012663   0.0016065   0.0019106
   0.0000000   0.0002451   0.0004665   0.0006657   0.0008446   0.0010045
   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000   0.0000000

Maximum absolute error
ans =  0.0032505
Plot results