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Homework Help: Advanced euler method query

  1. Aug 21, 2008 #1
    1. The problem statement, all variables and given/known data

    integrate dy/dx = (1+e^y)(1+x) from x=0 using the improved euler method taking step sizes of 0.125. compare the numerical solution of y(0.5) with the exact value

    3. The attempt at a solution

    Firstly to find the exact value I use seperation of variables and the initial condition y(0)=0 to find that y=-ln[-1+2e^(-x)e^{-(x^2)/2}]

    Subbing in x=0.5 yields 2.6518

    However, using an advanced euler calculator i found online tells me this:

    x_n y_n
    0.00000 0.00000
    0.12500 0.28560
    0.25000 0.67185
    0.37500 1.25597
    0.50000 2.45219

    That is, y(0.5)=2.45219

    I was just wondering if somebody would be able to confirm this is correct.

    Thanks!
     
    Last edited: Aug 21, 2008
  2. jcsd
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