ODE Parameter Estimation in Excel

Parameters (time constant and delay time) in a first order differential equation are fit to data in Excel. Excel solver is used to minimize a sum of squared errors between the data and predicted values by adjusting the two unknown parameters.

[@Debraj1978]

Perfect video. Thank you.

[@meeei85]

I have one question...if for example, several experiments have been performed to estimate the same parameters (maybe by providing different input values) where estimation for each experiment gives different final cost function value, how we can calculate the final parameter values? Is it OK to take average of all the values?

[@apm]

That is typically not a good idea to take an average. Can you use all of the data sets and come up with just one set of parameters to minimize the objective function (sum of squared errors)? That is a better way to combine data sets.

[@tawkirahmed2095]

great

[@ramiz2999]

I need to optimize k0, Ea and B in the pluf flow reactor:
d (Fa) / d (w) = (k0 * exp (-Ea / (R * T)) * (Ca / (1 + ((A * Ca) / Cb) + ((B * Cc) / Cb ))))
where Fa is molar flow, w is catalyst mass, and Ca and Cb are concentrations? dFa/dw is known, Ca and Cb are also known.
I need to do this in MATLAB.
Thanks in advance.

[@apm]

Please see apm.byu.edu for a couple courses that can help, especially dynamic optimization and design optimization. There are problems very close to yours.

[@k2btube]

How to do the same thing in R ? Any help would be highly appreciated

[@apm]

Here is some help for R: www.r-bloggers.com/learning-r-parameter-fitting-for-models-involving-differential-equations/

[@apm]

I'd recommend Python over R for scientific computing. There are additional Python (or MATLAB) tutorials on this topic at apmonitor.com/che263

[@k2btube]

Thanks a lot

[@drycell476]

and can we do this to second order diff eq?

[@apm]

Sure, 2nd order differential equations are possible: apmonitor.com/wiki/index.php/Apps/2ndOrderDifferential

[@ramiz2999]

Is this possible to do in Matlab and how? Thanks for your reply.

[@apm]

Sure, here are some tutorials: apmonitor.com/che263/index.php/Main/MatlabDataRegression and apmonitor.com/do (see Estimation sections)

[@ramiz2999]

@@apm Thank you.

[@user-ri4kp4om5e]

thank you very helpful