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Advanced Engineering Mathematics: Euler Method

  1. Sep 19, 2010 #1
    Do 10 steps. Solve the problem exactly. Compute the error (Show all details).

    The problems says do 10 steps, but 3-4 steps will suffice!

    Problem: y(prime) = (y-x)^2
    y(0) = 0
    h = 0.1

    I don't understand how to get the exact solution and what to do from there!
    I know that,
    f(x,y) = (y-x)^2

    And that u = (y-x)

    But from there, I am stuck!

  2. jcsd
  3. Sep 19, 2010 #2
    The differential equation can be solved. However it's not a very obvious solution since it is not linear.

    However you can get a bound on the error if you think about the problem in terms of Taylor series. Specifically what's the difference in using Euler's method versus a Taylor series?
  4. Sep 19, 2010 #3
    I don't think we're learning about Taylor series, but I just don't understand how we would solve the DE...

    I can probably apply to Euler's method after solving it...
  5. Sep 20, 2010 #4


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    Hint: What is u' equal to? Rewrite the original differential equation in terms of u.
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