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Math Help - Finite string Partial differential equation prob

  1. #1
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    Finite string Partial differential equation prob

    Consider the following finite string problem

    \mu_{tt} = \mu_{xx} where 0\le x\le 6

    \mu(x,0) = f(x) and \mu_t(6,t) = 0 for t\ge 6 with \mu(x,0) = f(x), and \mu_t(x,0) = 0

    where
    f(x) = 1 - |x - 3|, if |x - 3|\le 1 and is 0 otherwise.(sorry i dont know how to enter this as a array)


    give the equation of the solution for t = 2
    Last edited by r2dee6; February 23rd 2009 at 03:03 PM.
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  2. #2
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    Quote Originally Posted by r2dee6 View Post
    Consider the following finite string problem

    \mu_{tt} = \mu_{xx} where 0\le x\le 6

    \mu(x,0) = f(x) and \mu_t(6,t) = 0 for t\ge 6 with \mu(x,0) = f(x), and \mu_t(x,0) = 0

    where
    f(x) = 1 - |x - 3|, if |x - 3|\le 1 and is 0 otherwise.(sorry i dont know how to enter this as a array)


    give the equation of the solution for t = 2
    What course is this for? It looks like a straightforward separble equation. If you let \mu(x,t)= X(x)T(t) then the equation becomes XT"= X"T or T"/T= X"/X. Since the left hand side is a function of t only and the right hand side is a function of x only, each side must be a constant. Calling that constant \lambda, we have X"/X= \lamba or X"= \lambda X and T"/T= \lamba or T"= \lambda T.

    However, there is a problem with the additional conditionsl. Since this equation is second order in both x and t, you need two boundary and two initial conditions. You have only one of each.
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  3. #3
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    Its for the partial differential equations course. Im not sure how to go about doing it as I am self teaching myself the course
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