I am trying to make a table, in a range where \alpha = 0.01, 0.1,…1.5…2.0, and \mu=0.01, 0.1, 0.2,…1.0, 1.1, …10 for the following “Minimize” function, and compare it also to “NMinimize” with different methods:
What’s the recommended set of commands to do this?
I also tried D[\frac{\frac{64 b^5 \left(-16 b^5+4 b^3+\frac{3 \pi \sqrt{\frac{1}{b^2}} b}{\sqrt{1-b^2}}-\frac{6 \sin ^{-1}(b)}{\sqrt{1-b^2}}+6 b\right)}{\pi \left(96 b^5-96 b^7\right)}-\frac{4\, \alpha\, b^3}{(2 b+\mu )^2}}{b^2+1},\,b], and the using the result with Solve[result==0,b], but the evaluation doesn’t complete even after 10 minutes on an i7 machine with 16 GB RAM. Also doesn’t seem to work even with ND[ ].
If you post the Mathematica code (using the Code Sample icon) for the NMinimize and D[...,b] code above, you’re more likely to get responses. And is that (1/b^2)^(1/2)*b in the equation? That would simplify to 1 would it not? Having the code would eliminate such guesswork.
Sorry, I should have pointed out that this was a conditional expression Im[b^2] != 0 || Re[b^2] >= 0], and Mathematica calculated this from Integrate[(p^2 (p^2 + 1)^(3/2))/(b^2 + p^2)^4, {p, 0, Infinity}].
I am unsure how to do a loop in Mathematica to construct a table of the value of the the minimum expression, and the value of “b” where the minimum occurs, either using NMinimize or Minimize i.e. vary alpha from 0.01,0.02,…0.1,0.2,0.3…1.0,1.1…2.0, and vary [Mu] from 0.01,0.02,..0.1,0.2,0.3…1.0,1.1,…10. It’s an uneven grid, so alpha values go from 0.01 in increments of 0.01, then from 0.9 to 2.0 in increments of 0.1 etc.
An aside is the problem that evaluating D(-((4 alpha b^3)/(2 b + \[Mu])^2) + ( 64 b^5 (6 b + 4 b^3 - 16 b^5 + (3 Sqrt[1/b^2] b \[Pi])/Sqrt[ 1 - b^2] - (6 ArcSin[b])/Sqrt[1 - b^2]))/((96 b^5 - 96 b^7) \[Pi]))/(1 + b^2), b], then equating the result to == 0, and solving it – the calculation doesn’t complete even after 15 minutes. Same is the case if numerical differentiation is performed and the result equated to 0.
Many thanks Jim!
I am now trying to plot the list of triplets of the form {0.1,0.01,{1.99839,{b->0.0478935}}}. Being a newbie, I am transferring all of the values in another editor, substitute the -> and then plotting a 3D graph.
Is there a better way to combine Plot2D and Plot3D in the same (or sequential) declarative command?
“Table” command also appears to be working, but I have to check it thoroughly. I don’t know how to combine Plot in either the list from the first method or from the Table directly.
