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Math Help - Convergence of Eulers method.. Differential equations

  1. #1
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    Convergence of Eulers method.. Differential equations

    Prove that the approximation of Euler's method converges to the exact solution at any fixed point as h->0.
    - Because h->0 we know that the number of intervals h approaches infinity. I just can't seem to come up with a way of proving this theorem using algebra.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mathlete2 View Post
    Prove that the approximation of Euler's method converges to the exact solution at any fixed point as h->0.
    - Because h->0 we know that the number of intervals h approaches infinity. I just can't seem to come up with a way of proving this theorem using algebra.
    Look at the error analysis, the error per step should be bounded above by kh^2, for some k (depending on the function and the interval over which we are integrating) and the number of steps will be a/h where a is the length of the interval we are integrating over. So the total error at a fixed point will be bounded by kah, and so will go to zero as h goes to zero.

    RonL
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