Dsolve vs. ode45

[Michael Serban]

Hello everybody,
I have this system: dx1/dt = -8*x1-5*x2
dx2/dt = -5*x1-8*x2
which I solved using dsolve and I plotted the functions.
{This is the solution :
x1 = -1/2*exp(-3*t)+1/2*exp(-13*t)
x2 = 1/2*exp(-13*t)+1/2*exp(-3*t)
t = [0 2]}
Next, I solved the same system with ode45 and plotted the graphs.
Next I wanted to plot the difference, dsolve-ode45, and here the
problem put me down.
I got a message telling that convertion to double from ssym is not
possible. I forgot to tell you that I used
a tspan=[0 2] in ode45, and I tried to use the same same pitch in order
to get the value for the functions calculated analytically.
I am interested in graphing the difference x1(obtained with dsolve)
-x1(obtained with ode45) and the same for x2. I am looking for the
error between an analytically solved and numerically solved functions.
I tried to create an array with all the values of t used by the dsolve,
however I cannot create the array over 58 elements(I'm using Matlab5
student version) and all in all I have 169 values for t.
Is there a way to do it?
TIA,
Michael

[Cleve Moler]

Hi.

Try this. (This is the first time I've used "inline" with a
vector-valued function.)

F = inline('-[8 5; 5 8]*x','t','x')
[t,x] = ode45(F,[0 2],[0; 1]);
[x1,x2] = dsolve('Dx1 = -8*x1-5*x2', 'Dx2 = -5*x1-8*x2', 'x1(0)=0', 'x2(0)=1')
exact = [subs(x1,t) subs(x2,t)];
plot(t,x-exact)

The idea is to have ode45 determine the values of t it likes and then
substitute those values into the analytic solution obtained with dsolve.
The graph shows that, with ode45's default tolerances, the maximum error
is about 3e-5.

Nice example. Thanks.

-- Cleve Moler
mo...@mathworks.com

[Michael Serban]

Thank you for your time and suggestions.
I tried. For a tspan =[0 2] I 'm surpassing the limits of the student version.
Restricting t=[0 .5], I'm getting the messages: "Error using ==>plot. Ambiguous line
property: 's' " and " plot (t,x-exact).
I'll try some more, thank you anyway.
Regards, Michael