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differential equations - Monitoring the Evaluation of NDSolve: time to finish estimation


My problem is quite simple: I run a NDSolve with a system of many ODEs, a calculation that will run for many hours, and I would like to know the progress of the calculation while it goes on.



More precisely, calling f[n][t] the functions to be solved in the interval {tin,tfin}, It will be sufficient to print at regular intervals t the value of Sum[f[n][t]] for example, and possibly to save them as well. As a side effect, this will also give me an idea of when the calculation is going to end.


However I don't want to sacrifice a significant amount of runtime for this monitoring. One option could be really to split the calculation in intervals (a table of NDSolve) and print the intermediate results at each point. But I am afraid to have a significant overhead due to the reconstruction of the system of equations every time (I also use the method "EquationSimplification"->"Solve" which I believe transforms symbolically the system before integrating it) so I hope that some wizards among you could help me out providing an efficient solution to this problem using perhaps EvaluationMonitor or EventLocator or StateData ?


Any example will be appreciated.


EDIT: here is an example I just invented (the real example is more complicated).


M = 100;
Clear[P];
eqns := Table[
   P[k]'[t] == -(1/k) P[k][t] - 
     P[k][t]^2 Sum[Exp[-(k - q)^2/M] P[q][t], {q, 1, M}]
   , {k, 1, M}];


initial = Table[P[k][0] == 0.2, {k, 1, M}];

spos = NDSolve[Join[{eqns, initial}], 
   Table[P[k], {k, 1, M}], {t, 0, 100}, 
   Method -> {"EquationSimplification" -> "Solve"}, 
   PrecisionGoal -> 3, AccuracyGoal -> 3];


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