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## Does ode45 allow symbolic variables in its ode definition?

Asked by weiwei

### weiwei (view profile)

on 22 Jul 2011

The same as my title. Thanks a lot!

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## 1 Answer

### Jan Simon (view profile)

Answer by Jan Simon

### Jan Simon (view profile)

on 22 Jul 2011

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.

Walter Roberson

### Walter Roberson (view profile)

on 22 Jul 2011

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 Simon

### Jan Simon (view profile)

on 23 Jul 2011

@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

### weiwei (view profile)

on 24 Jul 2011

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.

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