Does ode45 allow symbolic variables in its ode definition?

The same as my title. Thanks a lot!

Answer 1

[Jan]

Inside the ODE function you can do what ever you want, as long as the output is numerical and has a certain degree of smoothness.

[weiwei]

Thanks for the quick reply. Actually, I have a number of odes.

y1' = f(y1,y2,y3,t,a,b,c)

y2'= g(y1,y2,y3,t,a,b,c)

y3' = h(y1,y2,y3,t,a,b,c)

And have some observed values of y1, y2, y3 at differnt times t. What I want to accomplish is to estimate the parameters a, b, c. My plan is to first establish some relationships(functions) between a, b, c and y1, y2, y3. And then use least squares minimization method to estimate a, b, c.

Do you think my logic of problem solving feasible in MatLab?

[Walter Roberson]

If you have known values at selected points for an ODE, but you do not know the form of the ODE, then I do not think it is possible to reconstruct the ODE uniquely without an infinite number of samples.

[Jan]

@Weiwei: It sound feasible. This is actually a standard parameter estimation of a boundary value problem on the subintervals. So start with a good coice of a,b,c, calculate the ODE and find better a,b,c by a variation or the evaluation of the sensitivity matrix. If your trajectories explode if a,b,c are far apart from the solution, use a multiple shooting method. The objective of your parameter estimation is than the distance between your trajectory from all mesaurements *and* the steps at each measurement point.

[weiwei]

As far as I know, the lsqnonlin function in Matlab is able to do parameter estimation using least square minimization. However, it requires an input of function definition. I cannot find a way to couple ode45 with lsqnonlin to do the above described work.