Nonlinear least-squares fitting of curve described by PDEs

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Xen
Xen 2017-7-20
编辑： Torsten 2017-7-21
Hi people. I would like to fit a curve described by a system of two 2nd degree partial differential equations (PDEs) using lsqnonlin. While it is simple to write your anonymous function when you have a single equation for your model, how can you do it when you have a system of PDEs, which do not have an analytic solution for the parameter of interest (the one to be fitted on the experimental data)? The PDEs have a number of free variables for which I would like to get the values that best fit the data. I could also try a better method than lsqnonlin, if there is one. Thanks

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Torsten
Torsten 2017-7-20
Although the description here is for ODEs, it can easily be adopted for PDEs:
https://de.mathworks.com/matlabcentral/answers/43439-monod-kinetics-and-curve-fitting
Best wishes
Torsten.
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Xen
Xen 2017-7-21
Despite that I can solve the PDEs for a random set of parameter values, I can't get it to work with lsqcurvefit. How can I pass my initial parameter estimates in the anonymous PDE function? I am thinking of just solve it for random parameters' combinations, compare with my experimental data and manually find the best solution...
Torsten
Torsten 2017-7-21
编辑：Torsten 2017-7-21
The "Anonymous Function" approach is the most flexible way to pass extra parameters to the PDE functions:
https://de.mathworks.com/help/optim/ug/passing-extra-parameters.html
Best wishes
Torsten.

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