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Help setting up a tricky system of ODEs

  1. Aug 5, 2009 #1
    Hi there
    I have been trying to set up a system of ODEs that are ultimately a solution to Burgers equation with a source term, and it boils down to:
    x' = 11v
    v' = f(H,H_x,s,s_x)
    where x = x(t), H = H(x,t), s = s(x) and H_x,s_x are the partial derivatives wrtx.

    The problem comes that I do not have an explicit formula for H, all I have is an equation for H_t, and the knowledge that (int H)' = int s

    By the chain rule,
    H' = x'H_x + H_t
    I know everything on the RHS except the H_x, so I thought since H also depends on time this needs to go into the system, giving
    x' = 11v
    v' = f(H,H_x,s,s_x)
    H' = 11vH_x + H_t
    which solves the problem of having H in the v' equation, but I am stumped as to how to deal with the H_x equation.

    I am looking to be able to solve this with ODE45 on matlab, which I have never used before.

    Any ideas?
  2. jcsd
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