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Math Help - Euler Approximation

  1. #1
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    Euler Approximation

    Use Euler’s method to estimate y (1.2), the solution to the IVP (initial value problem)

    y' = 2t - y, y (1) = -1, and step size h = 0.1.
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  2. #2
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    Quote Originally Posted by Oblivionwarrior View Post
    Use Euler’s method to estimate y (1.2), the solution to the IVP (initial value problem)

    y' = 2t - y, y (1) = -1, and step size h = 0.1.
    Where is the trouble?

    The approximate solution to the initial value problem

    \frac{dy}{dt} = f(t, y) where y(t_0) = y_0

    is given by y_{n+1} = y_n + h f(t_n, y_n).

    Therefore in your question:

    y(1.1) = y_1 = y_0 + h (2 t_0 - y_0) = -1 + (0.1) (2 - -1) = -1 + 0.3 = -0.7.

    y(1.2) = y_2 = y_1 + h (2 t_1 - y_1) = -0.7 + (0.1) (2.2 - -0.7) = -0.7 + 0.29 = -0.41.
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