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    Picard's Method of Successive Approximations

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    Please see the attached file for the fully formatted problems.

    Attached is a file with a three part successive approximation problem.

    The following problems are to use the method of successive approximations (Picard's)
    y x y fty tdt =+∫n− with a choice of initial approximation other than y0(x)=y0
    Using the stated initial value problem.
    (0) 1 y xyy =+=
    (a) y0(x)=e x
    (b) y0(x)=1+x
    (c) y0(x)=cos(x)
    I only need y1, y2 and y3 from the above.

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    Solution Preview

    First of all let's review the general Picard's iteration method:
    Let's assume that we have:

    Then we can say:

    This integral formulation can be used to construct a sequence of approximate solution to the problem. We must guess an initial approximate solution namely and then we can find an infinite sequence to approximate the ...

    Solution Summary

    Picard's method of successive approximations is used to find a sequence of terms.