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# Inverting dispersion relation

Posted 11 years ago
 Hi everyone,I'm trying to manipulate the dispersion relation for capillary-gravity waves, i.e.?² = Tanh[kh](gk + ?k³/?)in order to express k as a function of h. My first pick was to express h as a function of k h = (1/k) ArcTanh [?² (gk + ?k³/?)^(-1) ]and then try to invert it with Findroot, typing something like this :h[x_] := (1/x) ArcTanh[((70 \[Pi])^2)/ (9.81x + (0.0206 x³/950) )]hmax = 0.01;hmin = 0.001;dh = 0.0001;Sol = Table[{{b -> i}, FindRoot[i == h[x], {x, 0.001}]} // Flatten, {i, hmin, hmax, dh}];(I replaced some parameters with their experimental values) but this seems to stumble upon some convergence error. I'm not really familiar with Mathematica, and I found nothing that could help me in the doc. Does anyone have an idea on what I should try ?Thanks in advance for your replies !
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Posted 11 years ago
 >>Your Findroot line worked quite niceThanks, but it's not mine in fact, I've googled in the past when I had a need for it I.M.
Posted 11 years ago
 Your Findroot line worked quite nice, although my solution seems to become complex much quicker that I expected, but I can figure out a physical explanation for this.My deepest thanks !
Posted 11 years ago
 Hi,Please see the following posts, where inverse function was discussed:http://community.wolfram.com/groups/-/m/t/202130?p_p_auth=RqDuF3REhttp://community.wolfram.com/groups/-/m/t/195699?p_p_auth=z06oR5wZI.M.
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