1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Transcendental equation problem

  1. Aug 13, 2015 #1
    i have a transcendental equation and i have not a mathematique superieur formation ( i'm an hydraulic engeneer) and i want to resolve it but i can't so if you can help me with it !!

    the equation is : 2*x*n*ctg(2x)= x2 - n2 or (same equation) : (n*ctg(x)-x)*(n*tg(x)+x) =0

    n= constante ( i have this n.... in example n = 0.5 )
    xp = are the roots of equation above
     
  2. jcsd
  3. Aug 13, 2015 #2

    berkeman

    User Avatar

    Staff: Mentor

    Welcome to the PF.

    Did you mean to put this in the schoolwork forums? If it's for your work, it could be posted in the general Math forums...
     
  4. Aug 13, 2015 #3

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Such equations are normally solved by iteration, also known as trial and error.
     
  5. Aug 13, 2015 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    First: the ##\cot(2x)## function "blows up" (goes to ##\pm \infty##) at (infinitely many) finite values of ##x##, so that will give trouble in any numerical solution scheme. It is better to eliminate that problem by re-writing the equation as
    [tex] 2 n x \cos(2x) = (x^2 - n^2) \sin(2x) [/tex]
    Now a plot of both sides will reveal the approximate positions of roots, and these can be refined by various methods to get accurate values. There are infinitely many positive and negative roots.
     
  6. Aug 13, 2015 #5
    DEAR ,, RAY thnx for helping me,, if i understand u this infitely positive and negative roots are for this n in our example 0.5 .... AND if i tell you that xp the roots are depending to this index p like in series Σ ...because in my formula they wrote in it Xp like this ; X is h ( hn = are the roots of equation above) ,, the index p is n and n (n=0.5) in the equation is mew !!
    upload_2015-8-14_0-56-11.png

    the GENERAL EQUATION is ;
    upload_2015-8-14_1-0-45.png
    where in the left side constant i have it

    the right side this serie and THIS INDEX n batherd me a lot and complicate my equation because i dont know in wich number of n i stop my serie and also stop the root of the transcendental equation
     
    Last edited: Aug 13, 2015
  7. Aug 13, 2015 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I cannot understand anything you have written.
     
  8. Aug 14, 2015 #7
    lol ,, ok ,, my general formula is : my problem is hn roots of transcendental equation
    upload_2015-8-14_1-0-45-png.87288.png

    in PHI n i have hn ( hn is roots of the first transcendental equation that i wrote in first time )

    this is PHIn
    upload_2015-8-14_0-56-11-png.87287.png
    look at hn ,, now hn are roots of the transcendental equation upload_2015-8-14_15-32-29.png that u transform to 2nxcos(2x)=(x2−n2)sin(2x) i would tell you that the greek lettre eta ( upload_2015-8-14_15-33-54.png ) is n in first post thats all because i change variables lettre
     
    Last edited: Aug 14, 2015
  9. Aug 14, 2015 #8

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    η is called "eta"

    μ is called "mu", or "mew", as you prefer.
     
  10. Aug 14, 2015 #9
    lol see i forget very think lol
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted