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Re: Find all roots with FindRoot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126232] Re: Find all roots with FindRoot
  • From: Mikael Anderson <mikael.anderson.1969 at gmail.com>
  • Date: Thu, 26 Apr 2012 05:28:55 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <25227796.28036.1334923020612.JavaMail.root@m06>

I just wanted to give the RootSearch package a try but I wonder why
RootSearch misses some roots in the beginning of the solution when I change
the range as below:

>
> In[28]:= RootSearch[(Tan[Sqrt[theta]] - 2*Sqrt[theta]/(1 - theta)) ==
  0, {theta, 0, 1000}]

Out[28]= {{theta -> 0.}, {theta -> 5.43413}, {theta ->
   35.4046}, {theta -> 84.7952}, {theta -> 153.896}, {theta ->
   242.729}, {theta -> 351.298}, {theta -> 479.605}, {theta ->
   627.65}, {theta -> 795.435}, {theta -> 982.958}}

In[29]:= RootSearch[(Tan[Sqrt[theta]] - 2*Sqrt[theta]/(1 - theta)) ==
  0, {theta, 0, 10000}]

Out[29]= {{theta -> 0.}, {theta -> 84.7952}, {theta ->
   153.896}, {theta -> 242.729}, {theta -> 351.298}, {theta ->
   479.605}, {theta -> 627.65}, {theta -> 795.435}, {theta ->
   982.958}, {theta -> 1190.22}, {theta -> 1417.22}, {theta ->
   1663.96}, {theta -> 1930.44}, {theta -> 2216.66}, {theta ->
   2522.62}, {theta -> 2848.31}, {theta -> 3193.75}, {theta ->
   3558.93}, {theta -> 3943.84}, {theta -> 4348.49}, {theta ->
   4772.89}, {theta -> 5217.02}, {theta -> 5680.89}, {theta ->
   6164.5}, {theta -> 6667.85}, {theta -> 7190.94}, {theta ->
   7733.77}, {theta -> 8296.34}, {theta -> 8878.64}, {theta ->
   9480.69}}

/Mikael




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