Vector forcing a system of ODEs

Hi Mathworks,

I am using a time-dependent parameter in a system of ODEs - i.e. a vector is called at every timestep to force the system of differential equation. A good example of this being used is in the page for ode23, Example 3:

http://www.mathworks.co.uk/help/matlab/ref/ode23.html

Now my system is quite stiff, and so I must use ode15s to solve it. Under no forcing (or time-independent/constant parameters) the folowing code is able to solve the system, and produces output as in the literature:

[t,x]=ode15s(@transmission,tspan,[0,0,0]);

When I introduce this vector 'forcing', I add the following code to the transmission.m file:

f = interp1(ft,f,t);

And add the following arguments to transmission.m (or to the first line of transmission.m):

function xprime = transmission(t,x,ft,f);

Now when I call this function, I must first load the time and value vectors for the forcing vector - ft and f. Suppose these have been loaded into the workspace, then the following code should solve the system of differential equations:

[t,x] = ode15s(@(t,x) transmission(t,x,ft,f),tspan,[0,0,0]);

Although it doesn't work - " Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN."

It works better in ode45, but the solution vector is just "NaN", i.e. it didn't work. Can someone help me get ode15s to work for this forced system please :)

Moreover, can someone explain what the argument

@(t,x) transmission(t,x,ft,f)

to ode15s means/is doing - I am used to the normal arguments for ode functions but I don't understand this one.

Thanks,

Linford

Answer 1

[Linford Briant]

To update you all... I am even more baffled, because the solver seems to correctly find solutions to the system if I set

ft=[0:0.01:5e4];
f=0.01*cos(0.002*ft);

This is a massive simplification of the forcing vector I would like to use, but I used it as a test to see if my ode code was correct... looks like it is, but the problem may lie with the vector I am trying to force the system with.

Perhaps my vector has a timestep that is too small (0.025ms), but it works for a cosine vector of the same timestep.

So I am thinking that it is the forcing function that is the problem and leading to the error:

Warning: Matrix is singular, close to singular or badly scaled.
         Results may be inaccurate. RCOND = NaN.

But the system, when simulated in XPPAUT, is able to find a solution...

[Linford Briant]

It would seem maybe that I need to adjust tspan accordingly (duh!!) but if anyone has anything to add to this, that would be great!