# picard's method of iteration

• February 14th 2010, 08:07 AM
collegestudent321
picard's method of iteration
Hey guys, I'm having some trouble with this problem using picard's successive approximations:

y' = 2e^x - y, y(0) = 1

I thought the equation to begin the approximations would be:

y = 1 + integral of 2e^x - y

but when i make the substitution for y it doesn't work... any suggestions????
• February 14th 2010, 09:03 AM
Danny
Quote:

Originally Posted by collegestudent321
Hey guys, I'm having some trouble with this problem using picard's successive approximations:

y' = 2e^x - y, y(0) = 1

I thought the equation to begin the approximations would be:

y = 1 + integral of 2e^x - y

but when i make the substitution for y it doesn't work... any suggestions????

Yeah, you're good to go.

$
y_{n+1}(t) = 1 + \int_0^x 2e^t - y_n(t)\,dt\;\;(1)
$

Then start with $y_0(t) = 1$ and use eqn (1) recursively.