# Picard's Method of Successive Approximations

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.

https://brainmass.com/math/integrals/picards-method-successive-approximations-11153

#### 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.