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!

Asymptotic mathcing for a first order differential equation

  1. Jul 31, 2006 #1
    The first-order differential equation
    [tex]y' +(ex^2+1+1/x^2)y=0[/tex], with boudary value y(1) =1

    Using, asymptotic mathcing to study the behaviour of the sltion as e tends to +0, when x is not too large, the term [tex]ex^2 [/tex] is negligible so an approximate equation for y is
    [tex] y'_L +(1+1/x^2)y_L=0 [/tex].

    When x is large, [ tex ]ex^2 [ /tex ] is not negligible but [tex]1/x^2 [/tex] is. Therefore, an approximate equation valid as x tends to infinity is [tex] y'_R +(ex^2+1)y_R=0 [/tex].

    I think that te upper edge of the left region would be the largest value of x for which ex^2 is still small compared with 1. This would suggest that the left region consists of those x for which x<<e^-(1/2) as e tends to +0. But actually the region of validity of the left solution is e^(-1/3) (e tends to +0)....Can anyone explain this to me??

    Sams as the right region...Please kindly help
     
    Last edited: Aug 1, 2006
  2. jcsd
  3. Jul 31, 2006 #2

    jim mcnamara

    User Avatar

    Staff: Mentor

    I'm confused - [tex]e[/tex] is usually a constant
    [tex]e~=2.71828182845904523536028747135266249775724709369995...[/tex]
     
  4. Jul 31, 2006 #3
    sorry, I am referring e to be a small pertubation introduced...
    It would better to use a Greek word for it...
    but I have forgotten the word...
     
  5. Jul 31, 2006 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    e= epsilon: [itex]\epsilon[/itex]
     
  6. Jul 31, 2006 #5
    yes, HallsofIvy! Thank you.

    Do you mind helping me for this question?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Asymptotic mathcing for a first order differential equation
Loading...