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I used the $NMinimize$ instruction to calculate, but what I got was the dt value of the red circle. If I want to obtain the dt value of the green circle, how do I obtain it?

enter image description here

The code for generating the curve is as follows:

vc = Function[t, 
   23.999999999999996` + 
    55.082039324993595` E^(-267.92850868181444` t) - 
    79.08203932499359` E^(-186.61694586364015` t)];
condunequal = Abs[-1/2 dt (vc'[t + dt] - vc'[t])] <= 1/50000;
condequal = Abs[-1/2 dt (vc'[t + dt] - vc'[t])] == 1/50000;
RegionPlot[condunequal, {t, 0, 2/25}, {dt, 0, 0.0001}, 
 FrameLabel -> {t, dt}]
maxvc = NMinimize[{dt , condequal, 0 <= t <= 2/25, 
   0 <= dt <= 0.0001}, {t, dt}, MaxIterations -> 1000]
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  • $\begingroup$ Remove MaxIterations option and your will get the desired point $\endgroup$
    – Acus
    May 12 at 8:36
  • $\begingroup$ @Acus I removed $MaxIterations$ and obtained a result of 5.64137*10^-9. However, from the graph, it can be seen that the value of the green circle is approximately 5.3*10^-6, and the difference is still significant. $\endgroup$
    – chen chen
    May 12 at 8:50
  • $\begingroup$ It might be a precision issue, since you use very small numbers (10^(-117)) and do computation with machine arithmetic. $\endgroup$
    – Acus
    May 12 at 9:13
  • $\begingroup$ @Acus Sir, I tried using higher accuracy, but it didn't achieve the desired effect. $\endgroup$
    – chen chen
    May 12 at 11:09

1 Answer 1

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We modified the condition. 10^-10 <= dt <= 0.0001.

sol = NMinimize[{dt, condequal, 0 <= t <= 2/25, 
   10^-10 <= dt <= 0.0001}, {t, dt}, Method -> "DifferentialEvolution"]
Show[RegionPlot[condunequal, {t, 0, 2/25}, {dt, 0, 0.0001}, 
  FrameLabel -> {t, dt}], Graphics[{Red, Point[{t, dt}]}] /. sol[[2]],
  PlotRange -> All]

enter image description here

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  • $\begingroup$ Thank you very much! Using your method, the desired results were obtained. $\endgroup$
    – chen chen
    May 12 at 12:53

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