solve coupled differential equations mathematica

#Solve coupled differential equations mathematica full
#Solve coupled differential equations mathematica software

Because Mathematica is much more commonly-available as site licenses at universities, I am trying to develop routines to do the same thing in Mathematica, in a manner that does not require the user to be particularly fluent in Mathematica.

#Solve coupled differential equations mathematica software

This type of fitting procedure is extremely common in the natural sciences, and is a staple in such scientific software packages as OriginLab, SigmaPlot, and many others. Some of them will be fixed temporarily in order to allow one or more of the other parameters to migrate toward a better starting point, and will the later be allowed to vary. Some of these fixed parameters will be fixed because they are determined by way of separate experiments. The user then has an interface that allows them to adjust parameters, look at the comparison of the simulation to the data (including residuals), look at a sensitivity analysis of any of the parameters, and then, hopefully, tell the system to go off an try to optimize a set of parameters while holding others constant.

The user can then specify a Mathematica symbol that contains the experimental data to be fitting to. The package then automatically determines the differential rate equations that result from this sub-mechanism (shown at the top of the screenshot below), and then can add further time-dependent variables (in this case, absorbance 60, absorbance 70, and total absorbance), time-independent parameters (in this case, the extinction coefficients), and equations relating them to the automatically-determined differential rate laws. Here are some images from the interface:Īfter entering the chemical kinetics mechanism in standard chemistry notation, the user can select which steps of the mechanism are active: In this extension, I am providing an interactive interface to allow the user to fit experimental data with arbitrarily-complex chemical kinetics mechanisms. I am developing an extension to my Chemistry Package (info available here: ).

Hopefully this explanation will help explain exactly why I need it to smoothly handle such overparameterization. I don't want to rule out, though, that I may be doing something wrong, which is why I am asking here as well.)įuller context: The sense I am getting from some of the answers and comments is that the particular problem I am posing is poorly-formed because of the overparameterization. (In case this is a bug in Mathematica, I have submitted a bug report to Wolfram.

adding values for q and r to paramsForDataSet and to initialGuessĮverything else is identical, but this time the kernel crashes.

I am therefore adding a more complete example of the problem (the original question will be retained at the end).įirst, some sample data to fit to: sample = (0.002 + 101 t - 461000 t^2 + 2.218 10^9 t^3 -ģ.64 10^12 t^4 + 3.17 10^15 t^5) Exp ĭata = Table[ & dataset,

Unfortunately, trying to expand that solution to my more-complex problems also fails.

#Solve coupled differential equations mathematica full

And further, this solution works perfectly without having to correct for the differing magnitudes of the parameters or accounting in any explicit way for the overparamaterization.Īnother Edit: Added full context of the problem to the end of the post.Įdited to add: The choices of Method given in the comments and in the answer provided by Tim work for the example I originally provided, and I thank all of you for those suggestions.

Huzzah! It appears that the crashing behavior was coming from some inability of the fitting routines to correctly calculate the gradient. Can someone send some help? Thank you so much.Final Edit: I have found a solution! Specifying Method->'LevenbergMarquardt', Gradient->'FiniteDifference' gives the behavior I am looking for. I don't know much about mathematica and this problem is untractable without numerical methods. Here, $V$ and $Y$ are functions that only depend on $r$, i.e., $V=V(r)$ and $Y=Y(r)$. I am trying to solve the following system of two coupled partial differential equations (both equations equal 0):