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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)
[EQUATION]
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 Summary

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

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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 ...

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