(adsbygoogle = window.adsbygoogle || []).push({}); 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:

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 :)

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# Method of characteristics

Can you offer guidance or do you also need help?

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