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Mathematica chaplygin gas model

  1. Jun 3, 2012 #1
    Hey guys,

    I'm using Mathematica to plot some graphs and I'm having a bit of a hard time.

    First I have to solve the following equation,

    2/3 a^2 b''[a] + (1 - w[a]) a b'[a] - (1 + w[a]) (1 - 3 c w[a]) b[a]

    Boundary condition b'[0.0001]=0
    Where;

    w[a_] := 2*a^(3*(1 + c))/(1 + 2*a^(3*(1 + c)));

    (c=1) (c is a variable but let's consider a particular instance c=1)

    a goes from 10^-4 to 1000 in a log scale.

    I want to plot b[a]/b[0.0001] vs. a

    I've so far written a simple code but it is with errors.

    c = 1;
    w[a_] := 2*a^(3*(1 + c))/(1 + 2*a^(3*(1 + c)));
    fun = 2/3 a^2 b''[a] + (1 - w[a]) a b'[
    a] - (1 + w[a]) (1 - 3 c w[a]) b[a]
    F[a_] = DSolve[{fun == 0, b'[10^(-4)] == 0}, b, a]
    L = LogLinearPlot[Evaluate[F[a]/F[0.0001]], {a, 10^-4, 10},
    PlotRange -> All];
     
  2. jcsd
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