Hello, I would like to ask about how WorkingPrecision option works in FindRoot. Basically, I have two functions \theta and \phi on a lattice N1xN1. On each site I have two equations like below with some boundary conditions, so I use FindRoot to solve all of them. I've got warning message like on second picture and result was not quite physical so I decided to increase WorkingPrecision, but when I change it to whatever except MachinePrecision calculation freezes(I checked 3,6,16,50). As I understood by changing WorkingPrecision I simply change number up to which Mathematica holds the order during computation(maybe there are some nuances like this is order in hexadecimal system but nevertheless), but it looks like there is something else. I would be very grateful if someone can help me. Notebook is attached, I highlighted Findroot with red.
