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Math Help - Need help with Higher derivative Euler method

  1. #1
    Member zzizi's Avatar
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    Need help with Higher derivative Euler method

    Hi

    I am trying solve numerically the equation using the higher derivative Euler method with 3 terms:

    y' = 2x +y

    with y(0)=0

    h = 0.1 and aiming to to estimate y(0.5)


    Can anyone who is familiar with this method offer some help in formulating the terms?

    I have worked out the following:

    y' = 2x +y
    y'' = 2

    So, yi+1 ≈ yi + (0.1)(2)xi + (0.1)yi + (0.1)^2/2! (2)

    Is this correct?
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  2. #2
    MHF Contributor
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    Re: Need help with Higher derivative Euler method

    Hey zzizi.

    Hint: When you are differentiating d/dx (2x + y) then you get y'' = d/dx (2x + y) = 2 + dy/dx = 2 + 2x + y.

    Also what is your formula for updating y(x+h) given y(x) for your Euler Method update?
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