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Homework Help: Non-dimensionalization of diff. system

  1. Dec 20, 2008 #1
    I don't have any experince in normalizing when the equations depend on eachother, so was hoping someone could tell me if what I have done is correct, and if not what the problem is :)

    1. The problem statement, all variables and given/known data
    I need to non-dimensional the following differential equations.

    L1:= dn/dt = (a-b-k*y)*n
    L2:= dy/dt = l*n-d*y

    to
    dN/dT= (D-Y)*N
    dY/dT = N-Y
    knowing that D = (a-b)/d.

    3. The attempt at a solution
    I start with inserting

    n = k[n]*N,
    y = k[y]*Y,
    t = k[t]*T

    L1:= d(k[n]*N))/d(k[t]*T) = (a -b-k*(k[y]*Y)*k[n]*N

    L2:= d(k[y]*Y)/d(k[t]*T)= l*(k[n]*N) - d*k[y]*Y

    I look at L2 first, and divide with k[y]/k[t] on both sides.

    Then I set l= k[y]/(k[n]*k[t]) and d=1/k[t]

    getting dY/dT = N-Y

    next I look at L1, and divide with k[n]/k[t] on both sides and inserting k[t] = 1/delta ( which I found above)

    getting
    dN/dT = ((a-b)/(d) - (k*(k[y]*Y))/(d))*N

    I now put D = (a-b)/d and k = d/k[y]
    getting

    dN/dT= (D-Y)*N (which is what I wanted)

    Is this the correct way of approaching it?
    Thanks Louise
     
    Last edited: Dec 20, 2008
  2. jcsd
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