# Numerically solving coupled DEs?

1. Sep 20, 2006

### gyver

Hi folks!

I'm trying to (numerically) find a steady-state solution for $$N_b$$ and $$N_w$$ in the following set of coupled DEs using the software package Matlab:

$$\left{ \begin{array}{l} \frac{\delta N_b}{\delta t} = P_b(N_b) - N_b \cdot \left( \frac{1}{\tau_b} - \frac{1}{\tau_c}D \right)\\ \frac{\delta N_w}{\delta t} = \frac{N_b}{\tau_c} - \frac{N_w}{\tau_w(N_w)} - P_w(N_w) \end{array} \right.$$

where $$\tau_b$$, $$\tau_c$$ and $$D$$ are constants. Which way would be the right one to go?

Last edited: Sep 20, 2006
2. Sep 20, 2006

### omagdon7

Remove the dimensions and write a program to do RK4 unless this is just for a class in which case RK2 or Euler's with really small step is easier.

3. Sep 20, 2006

### HallsofIvy

Staff Emeritus
I'm don't know MatLab but I'd run two Runge Kutta 4th order (RK4) algorithms simultaneously, using the current values for Nb and Nw in each formula.

4. Sep 22, 2006

### J77

What form do $$P_b$$ and $$\tau_w$$ take?