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!

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
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: Method of characteristics
Loading...