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Asymptotic solution

  1. Jun 25, 2009 #1
    I have the solution (a potential) for a nonlinear differential equation found at r=0. How can I calculate the asymptotic potential at r->infinity?

    Thanks in advance
    MS
     
  2. jcsd
  3. Jun 26, 2009 #2
    What is the equation? What is the solution? There is waay too little data here.
     
  4. Jun 26, 2009 #3
    This is the nonlinear equation

    diff(y(r),r,r)+2*diff(y(r),r)/r+486*polylog(3/2,-exp(1-1/43*y(r))) = 0;
    Initial conditions: y(0) = 0, D(y)(0) = 0.

    Sol:1.05375994-.2150397042*r+.2150397042*r^2

    Thank you
     
  5. Jun 26, 2009 #4
    umm... It doesn't seem like your solution satisfies the initial condition: y(0)=0. Other than that, It's just a parabola, so there's no asymptotic behavior - it simply diverges...
     
  6. Jun 26, 2009 #5
    There is asymptotic potential in the form of some ln function. But I don't know how to calculate it. and regarding potential at y(0), i will recheck my solution.
    But my question is that if I have a solution for this differential equation at initial conditions, how can i get an asymptotic solution at r approaches infinity?

    Thanks for your time
    MS
     
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