Question

What are picard's iterates in differential equation?

Answer 1

I have the following system:

y′(t)=x2(t)−x(t)

x′(t)=y(t)

It comes from the second order ode

x′′(t)=x2(t)′x(t)

I am asked to do the first four Picard iterations starting from the solution

ϕ0(t)=(−12,0)

I can do Picard iterations for a simple first order ode, but I am not able to generalize it to a system where the two equations depend on each other, and I cant find any examples or theory that tells the algorithm to help me in this case.

differential-equations