I need to find the 50 first roots of a transcendental equation. I use Table and FindRoot, so I find repeated positives and negatives values in a list, but I want only the 50 first positives and differents roots. Somebody can help me?


closed as off-topic by J. M. will be back soon Aug 22 '15 at 12:42

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    $\begingroup$ Please provide the code you are using, in order that readers can assist you with it. $\endgroup$ – bbgodfrey Apr 19 '15 at 16:28

For example, this is reasonably fast on the following example:

eqn = Sin[x] + 0.5 Cos[10 Pi x];

sols = FindRoot[eqn, {x, #}] & /@ Module[{n = 0},
    NDSolve[{y'[x] == D[eqn, x], y[0] == (eqn /. x -> 0),
      WhenEvent[y[x] == 0, Sow[x]; If[++n >= 50, "StopIntegration"]]},
     {}, {x, 0, Infinity}]
    ][[2, 1]]
(*  {{x -> 0.0534047}, {x -> 0.140935},..., {x -> 15.5391}}  *)

Plot[eqn, {x, 0, Max[x /. sols]}, Epilog -> {Red, Point[{x, 0} /. sols]}]

Mathematica graphics

  • $\begingroup$ (# - 2)^2 (# + .5)^2 - 625/256 &[x], it seems that not all the roots can be found for this function. $\endgroup$ – Αλέξανδρος Ζεγγ May 16 '17 at 8:13
  • $\begingroup$ @AlexanderZeng Use NSolve for polynomial equations. (Why such a complicated example? It's pretty clear that any method that relies on sign change is going to fail on even-multiplicity roots, so (x-2)^2 is sufficient.) If you're looking for a similar approach for a transcendental equation, you might use f[x] * f'[x] and keep only those seeds for which Abs[f[x]] is small. $\endgroup$ – Michael E2 May 16 '17 at 11:07

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