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looking for numerical method to solve equation involving PolyLogs

Posted 9 years ago

I have this:

VG = Table[i, {i, -30, 30, 0.1}]

VG - (Vch +A* (-PolyLog[2, -E^-BVch] + PolyLog[2, -E^BVch]) ) == 0

A and B are constants. I'm trying to solve for Vch (another table). Any suggestions?

thanks.

POSTED BY: Ethan Torrey
2 Replies

Are you trying to solve for exact values, or get a best fit in terms of least squares? It looks like the latter since there are so many points. I'd suggest checking FindFit if that is in fact the case.

POSTED BY: Daniel Lichtblau
Posted 9 years ago

Daniel-

Thanks for the quick reply. I have little Mathematica experience and so wanted to try to figure out how to carry out your suggestion before asking for further help. Sadly- still stuck. I reduced the size of my input table to simplify things. Am I just misunderstanding the syntax for FindFit? Here's what I get:

In[15]:= VG = Table[i, {i, -30, -29, 0.1}]

Out[15]= {-30., -29.9, -29.8, -29.7, -29.6, -29.5, -29.4, -29.3, -29.2, -29.1, -29.}

In[16]:= FindFit[%, VG - (Vch + (-PolyLog[2, -E^-Vch] + PolyLog[2, -E^Vch])) == 0, Vch, VG]

During evaluation of In[16]:= General::ivar: -30. is not a valid variable. >>

Out[16]= FindFit[{-30., -29.9, -29.8, -29.7, -29.6, -29.5, -29.4, -29.3, -29.2, -29.1, -29.}, {-30. - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.9 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.8 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.7 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.6 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.5 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.4 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.3 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.2 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29.1 - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch], -29. - Vch + PolyLog[2, -E^-Vch] - PolyLog[2, -E^Vch]} == 0, Vch, {-30., -29.9, -29.8, -29.7, -29.6, -29.5, -29.4, -29.3, \ -29.2, -29.1, -29.}]

POSTED BY: Ethan Torrey
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