Nonlinear least-squares fitting of curve described by PDEs

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Xen 2017-7-20

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https://ww2.mathworks.cn/matlabcentral/answers/349553-nonlinear-least-squares-fitting-of-curve-described-by-pdes

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 2017-7-20

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https://ww2.mathworks.cn/matlabcentral/answers/349553-nonlinear-least-squares-fitting-of-curve-described-by-pdes#answer_274871

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 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...