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Rev

$\begingroup$ Thanks a lot for your so helpful and detailed answer. However, the equation is not zero and that's what is worrying me! Well, let me phrase my worry: how do I make sure that the numerical solutions are indeed near actual solutions? I guess I must use some sort of certification here! In that case, probably it is not a thing to discuss in this forum? $\endgroup$

John
– John

2014-06-23 21:34:46 +00:00
Commented Jun 23, 2014 at 21:34
$\begingroup$ @John I feel foolish: See the update. You can use Solve on the infinite-precision equation to verify the solutions -- or even find them! You could make a plot near an approximate zero. For example, With[{x0 = N[x /. solexact[[57]], 200]}, With[{eps = 2^Floor@Log2[Abs[$MachineEpsilon x0]]}, ListLinePlot[{Table[{k, Re@eP /. x -> x0 + k eps}, {k, -2, 2, 1/5}], Table[{k, Im@eP /. x -> x0 + k eps}, {k, -2, 2, 1/5}]}, ImageSize -> {Automatic, 150}]]]. Then you can see where it crosses. $\endgroup$

Michael E2
– Michael E2

2014-06-23 23:44:58 +00:00
Commented Jun 23, 2014 at 23:44

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