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I am solving a PDE

  1. May 31, 2008 #1
    1. The problem statement, all variables and given/known data

    oh! after trying to re-solve a PDE I reached this:


    2. Relevant equations
    [tex]\sum\frac{4}{((2n-1)\pi)^2} (a+\frac{4(-1)^{n+1}}{(2n-1)\pi}) cos(\frac{2n-1}{2}\pi x) [/tex]

    n goes feom 1 to [tex]\infty[/tex] and "a" is a constant value.

    3. The attempt at a solution
    the solution i am trying to reach is:

    [tex]=\frac{1}{2} (1-x^{2}+(1-x)a)[/tex]

    but i don't know how?
    can anyone help please?
     
  2. jcsd
  3. May 31, 2008 #2

    HallsofIvy

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    What is the Fourier series for [tex]\frac{1}{2} (1-x^{2}+(1-x)a)[/tex]?
     
  4. Jun 2, 2008 #3
    thanx for suggestion my buddy.
    u know the orginal problem is a heat equation - one dimentional and time dependent-

    [tex]T_{xx}+j^{2}=T_{t}[/tex]
    [tex]T_{t}=-1/2j\frac{b}{cL}[/tex]
    [tex]T(1,t)=0[/tex]
    [tex]T(x,0)=0[/tex]

    j,c,b are constant and 0[tex]\leq[/tex]x[tex]\leq[/tex]1

    i solved the problem to here:

    [tex] T(x,t)= j^{2} \sum (\frac{1}{\lambda_{n}^{2}}) \times \frac{b}{cL}+ \frac {2 \times -1^{n+1}}{\lambda_{n} cos(\lambda_{n}x + j^{2} \sum \frac{-1}{(\lambda_{n})^{2}}(e)^{-\lambda_{n}t} \left[\frac{b}{cL}+ \frac {2\times -1^{n+1}}{\lambda_{n}\right] cos(\lambda_{n}x)[/tex]
     
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