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Math Help - The Euler's Method equation

  1. #1
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    The Euler's Method equation

    In the Euler's Method section of my textbook, there are two equations mentioned (see attachment). I was wondering if there was any difference between the two, or if they refer to the same thing.

    The help would be appreciated
    Attached Thumbnails Attached Thumbnails The Euler's Method equation-screen-shot-2010-05-13-2.55.03-pm.png  
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  2. #2
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    Quote Originally Posted by DJ Hobo View Post
    In the Euler's Method section of my textbook, there are two equations mentioned (see attachment). I was wondering if there was any difference between the two, or if they refer to the same thing.

    The help would be appreciated
    They are different equations the second being more general than the first.

    In y_{n+1}= y_n+ hF(y_n, t_n) we are ignoring the fact that t is a continuous variable and just looking at specific points, t_0, y_0), (t_1, y_1), etc. separted by distance h along the t axis.

    In y(t+ h)= y(t)+ hy'(t) we are retaining the continuity of t- here t could be any number. Of course, if we take t_0 to be some specific value, then define y_0= y(t_0), t_1= t_0+ h, y_1= y(t_1), t_2= t_1+ h= t_0+ 2h, y_2= y(t_2), etc. then the second equation becomes the same as the first.
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  3. #3
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    Ahh yes, I understand. Thanks for that.
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