Atmospheric pressure example 

analytical solution

>>> import math
>>> math.exp(-0.12164*0.125)*1013.25
997.96007001738064
>>> math.exp(-0.12164*0.250)*1013.25
982.90086488931206

~/P/thesis/kthorder$ python firstorder.py "x*-0.12164" 1013.25
[997.84353375000001, 997.84399613405003]
[982.67132281933129, 982.67224055688177]

octave 
octave:1> function dy = atmospheric(y,x)
> dy(1) = y(1) * -0.12164
> endfunction
octave:2> t=[0:0.125:0.250];
octave:3> x0=[1013.25];
solved = lsode("atmospheric", x0, t);
solved =
   1013.25
    997.96
    982.90

~/P/thesis/kthorder$ python firstorder.py "x*x" 1.0
[1.125, 1.28125]
[1.283203125, 1.6778564453125]

octave:1> function dy = moore(y,x)
> dy(1) = y(1) * y(1)
> endfunction
octave:2> t=[0:0.125:0.250];
octave:3> x0=[1.0];
octave:4> solved = lsode("moore", x0, t);
octave:5> solved
solved =
   1.0000
   1.1429
   1.3333