- #1
bndnchrs
- 29
- 0
Homework Statement
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]
Homework Equations
None other than the usual method of characteristics stuff
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.