Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 3.1

Nonautonomous Linear Systems

Mathematics — Calculus · picard-iterates-linear-system

Problem

Let

A

be an

n \times n

matrix over

\mathbb{R}

, and let

x_0 \in \mathbb{R}^n

. Calculate the Picard iterates for the initial value problem

x' = Ax, \quad x(0) = x_0,

and show that they converge uniformly to the exact solution on every closed, bounded interval of the form

[-T, T]