partial differential equation

Discussion in 'Math' started by jav_dec80, Oct 7, 2013.

  1. jav_dec80

    Thread Starter New Member

    Oct 6, 2013
    2
    0
    Good morning

    Please help me to solve
    Ut = 3Uxx 0 < x < 2 and t > 0
    Ux(0 , t ) = Ux( 2 , t ) = o
    U (x , 0 ) = 3x

    Thanks
     
  2. blah2222

    Well-Known Member

    May 3, 2010
    554
    33
    Is your goal to solve this analytically on paper or are you able to use numerical methods such as finite difference in MATLAB?

    Tidying things up, is this what you're given?

    0 < x < 2 & t > 0

    <br />
\frac{\partial u}{\partial t} = 3\frac{\partial^{2} u}{\partial x^{2}}<br />

    <br />
\frac{\partial u}{\partial x}(0, t) = \frac{\partial u}{\partial x}(2, t) = 0<br />

    <br />
u(x, 0) = 3x<br />
     
    jav_dec80 likes this.
  3. jav_dec80

    Thread Starter New Member

    Oct 6, 2013
    2
    0
    My goal is to solve this analytically
    Please help if u can
    Thanks and Regards
    Jav
     
  4. WBahn

    Moderator

    Mar 31, 2012
    17,721
    4,788
    It's been many moons since I solved PDEs. My first (feeble) thought would be to assume an exponential form of a solution and see what that does.
     
  5. blah2222

    Well-Known Member

    May 3, 2010
    554
    33
    Post the work that you have done to try and solve this. We can go from there.
     
  6. ramueller11

    New Member

    Dec 13, 2013
    4
    0
    The PDE is a well-known PDE: the heat equation or the diffusion equation. There most common solution and can be derived assuming the solution u(x,t) = X(x)T(t). The the other analytical solution involves the complementary error function. I suspect it involves Laplace/Fourier Transforms. However, the latter solution holds only for boundary conditions of 0 at x = +- infinity and intial conditions of a delta function. So this probably leaves the former as the likely solution which you will find is a Fourier series involving only cos(x) functions due to the boundary condition.

    See this: http://en.wikipedia.org/wiki/Parabolic_partial_differential_equation
     
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