# Pade Approximation and it's Applications

1. Jun 6, 2006

### LLT

Pade Approximation states that a power series can be written as a rational function. Which is a series divided by another series.
(An easy example of this will be the geometric series with mod'r' < 1)

I've read books about the abstract bit of this. But I am completely stuck when it goes onto applications.

How does pade approximation help solving PDE and ODE? And sometimes, people optain a power series solution for PDE and ODE, (of polynomials of x) how did they do that?

I would also very much like to understand the Navier-Stokes equations.. but this can come later.

2. Jun 8, 2006

$$\frac{d x(t)}{dt} = Ax(t) + bu(t) \;\;\;\; , \;\;\;\;\;y(t) = c^Tx(t)$$