1. Not finding help here? Sign up for a free 30min 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!

PDE: The Eikonal Equation method of characterstics, etc.

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data
    I need to solve the Eikonal Equation [tex]c^2(u_x^2 + u_y^2) = 1[/tex]

    Initial condition u(x,0) = 0 C(x,y) = |x|, but x>0 to essentially C = x


    Oh. And the solution is given as [tex]\ln{\frac{\sqrt{x^2 + y^2} + y}{x}}[/tex]
    2. Relevant equations
    None other than the usual method of characteristics stuff


    3. The attempt at a solution

    I can go through the method of characteristics and I get stuck with solving for X(s,t) and Y(s,t) at:

    dX/dt = P*X^2
    dY/dt = X^2*1/s
    dP/dt = -1/X

    s is a parameter here, not a variable. I'm really stuck, and need some fresh insights on this one, I've been working it for too long that I'm missing something critical.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: PDE: The Eikonal Equation method of characterstics, etc.
  1. 1D wave equation PDE (Replies: 0)

Loading...