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Homework Help: Difficulties with solution/plotting of a PDE.

  1. Apr 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Question attached

    2. Relevant equations

    3. The attempt at a solution

    I'm mostly wondering with c) and also want to check if my solution is correct.

    My solutions for this question are:

    u(x,t)= -1/2 for x <= -1/2*t
    = 1 for -t < x < 1-t
    = 1/2 for x => 1/4*t+1

    lastly, with c), I'm just wondering how to plot 3 space curves on the same axes?(as there are 3 different solutions)

    thanks in advance.

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    Last edited: Apr 23, 2010
  2. jcsd
  3. Apr 24, 2010 #2


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    It depends on what software package you are using. In Maple it would be something like this. Call your three functions f(x),g(x), h(x)


    where a and b are whatever limits you want.
  4. Apr 24, 2010 #3
    Hi LCKurtz, thank you for your help ones again!

    yes, I'm using Maple, as it is the only available computing package to me.

    I tried plotting it the way you said, and it came out looking wrong, but I think it's because I'm doing it wrong, would this sort of PDE be more suitable with a 3D plot?

    Below I've also done a 3D plot, where the xi ranges I worked out by inputting t=0,2,4 respectively to get the lowest and highest possible domain for x for each interval of x. Is there a way to tell Maple to join up the 3 sets of lines so that you can see where there are jump discontinuities?


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  5. Apr 24, 2010 #4


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    First, I am not a PDE expert so I'm not sure how much help I can give you. You are to plot your solution for t = 0, 2, and 4. With t fixed you have just a function of x. So why would you use space curve instead of just plot.

    But a more serious question I have is, consider your solution for t = 2. Then

    u(x,2) = -1/2 for x <= -1
    = 1 for -2 < x < -1
    = 1/2 for x >= 3/2

    What if x is between -2 and -1, do you use the first or second part? What about x between -1 and 3/2, what is u there? It doesn't look like your solution is well defined.
  6. Apr 24, 2010 #5
    Oh you're quite right, but I have checked my inequalities and followed the example we've been given step by step, is there anyway to rearrange the inequalities so that the solution is defined for all intervals?

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