Here I have one problem how to solve numerically equation for different values of one parameter x. I used just two digits because of length, but for x=0.57 I should have one real root and for others 0.6, 0.7 ... complex roots. These seven points I want to plot in complex (Re,Im) plane with line. The first problem is that NSolve doesn't work, with Reduce I can obtain some results with problems. Another problem is to understand what's happen when x-> Infinity
x = {0.57, 0.6, 0.7, 0.8, 0.9, 1, 1.1};
NSolve[1/Sqrt[y]
0.02 (1.`5. I (64.`5. + 2.10 Sqrt[y]) Sqrt[-64.`5. +
4.21 Sqrt[y]] + (64.`5. - 2.10 Sqrt[y]) Sqrt[
64.`5. + 4.21 Sqrt[y]]) Sqrt[-64.`5. + 4.21 Sqrt[y]] Sqrt[
64.`5. + 4.21 Sqrt[y]] + 0.03 Sqrt[y] - # == 0, y] & /@ x
NSolve
doesn't work". You might find this formulation useful though.soln[x_] := NSolve[(1/ Sqrt[y] 0.02 (1.
5. I (64.5. + 2.10 Sqrt[y]) Sqrt[-64.
5. + 4.21 Sqrt[y]] + (64.5. - 2.10 Sqrt[y]) Sqrt[ 64.
5. + 4.21 Sqrt[y]]) Sqrt[-64.5. + 4.21 Sqrt[y]] Sqrt[ 64.
5. + 4.21 Sqrt[y]] + 0.03 Sqrt[y] - # == 0), y] &[x]` $\endgroup$NSolve
tells me that there are no roots, whileReduce
returns solutions. I tested on a rationalized version of the system but I didn't verify if the results returned byReduce
are correct. $\endgroup$SetPreicision[..., 100]
on your equation and useWorkingPrecision -> 100
inNSolve
. Then it will be able to return the same resultsReduce
gives you. Sorry, no time for writing this in an answer. Anyone reading this feel free to post it. $\endgroup$x
. The issue I believe is in verification-- without using high precisionNSolve
seems to think the roots it finds are all parasites. $\endgroup$