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Solve Wave Function - Computational

  1. Nov 24, 2014 #1
    1. The problem statement, all variables and given/known data

    Hi all,

    I've been working on this assignment for some time now and seem to be stuck before I even get going!
    So,

    The wave equation:

    d^2 u(x,t) / dx^2 = d^2 u(x,t) / dt^2

    can be written as:

    du/dt = v
    dv/dt = dw/dx
    dw/dt = dv/dx
    w = du/dx

    I need to solve this using Python. I'm going to do it using Euler's method.

    Some initial conditions:

    u(x,0) = e^(-x^2 / 2*sigma^2)

    sigma = 0.1

    du(x,0) / dt = 0

    du(x,0) / dx = -100x*u(x,0)

    _________

    What I've figured, is that in order to implement Euler I need to use the u_dot, v_dot and w_dot as a vector of your RHS. So you use this do calculate the next time step since

    U(u,v,w)n+1 = U(u,v,w)n + dt*RHS(u_dot,v_dot,w_dot)

    u_dot being du/dt btw

    However, I have no idea how to actually do this, I'm completely thrown :(
    I've been trying to get somewhere on paper and on the computer coding and neither has really given me anything I can use. How do I find U(u,v,w)n for a start?? and the RHS is d^2u/dt^2 i think.. How am I ever going to put that into python :S :S :S??

    Any help and hints would really be helpful the deadline is coming up soon and I'm very stumped here.

    Cheers all
     
  2. jcsd
  3. Nov 24, 2014 #2
    Also, everywhere I look the wave function equation is written d^2u / dt^2 = c^2 * d^2u / dx^2

    I have no idea why the one in my question is different. Any ideas?
     
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