# Picard Iteration

• Apr 30th 2011, 12:24 PM
PatrickM
Picard Iteration
I'm doing some revision and I'm having some trouble understanding the principle behind picard's iteration.I tried to do some practice by tackling the following problem but I got nowhere as I don't know with what should I substitute f(s,u(s)) in the integral.
The problem states the following:
u'= v and v'= −u
with initial conditions u(0) = 1 and v(0) = 0, find an approximate solution by
performing 4 steps of Picard iteration and compare the results with the actual solution.
If someone has the time and patience to enlighten me with a step by step explanation that will be incredible.
Thanks at least for taking the time to read this
• May 12th 2011, 07:51 AM
Sudharaka
Quote:

Originally Posted by PatrickM
I'm doing some revision and I'm having some trouble understanding the principle behind picard's iteration.I tried to do some practice by tackling the following problem but I got nowhere as I don't know with what should I substitute f(s,u(s)) in the integral.
The problem states the following:
u'= v and v'= −u
with initial conditions u(0) = 1 and v(0) = 0, find an approximate solution by
performing 4 steps of Picard iteration and compare the results with the actual solution.
If someone has the time and patience to enlighten me with a step by step explanation that will be incredible.
Thanks at least for taking the time to read this

Dear PatrickM,

I don't think this problem could be done using Picard iteration method. The Picard iteration method may be applied for a first order differential equation with a given boundary condition. However in this case there are two first order differential equations with unknowns v and u. So you could solve this system by representing the two equations in matrix form.