Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Method of characteristics

  1. Jun 20, 2011 #1
    1. The problem statement, all variables and given/known data

    For the given PDE:

    [itex]\partial_t u+\frac{1}{2}\partial_x u=0[/itex]

    Where:

    [itex]u(0,t)=-1/2t\;;\;t>0[/itex]

    [itex]u(x,0)=x\;;\;0\leq x\leq2[/itex]

    [itex]u(x,0)=4-x\;;\;2<x\leq4[/itex]

    [itex]u(x,0)=0\;;\;4<x[/itex]


    3. The attempt at a solution

    Characteristic equations give :

    [itex]x=\frac{1}{2}t+x_0[/itex]

    [itex]u(x,t)=f(x-\frac{1}{2}t)=f(x_0)=const.[/itex]

    Which,on the (x,u) graph would look something like:

    attachment.php?attachmentid=36605&stc=1&d=1308594710.png

    Is this correct?

    The next thing i have to do is to find the solution to it via Lax-Wendroff scheme,but i won't be bothering anyone with that :)
     

    Attached Files:

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted