# Numerically solving coupled DEs?

#### 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?

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#### 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.

#### HallsofIvy

Homework Helper
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.

#### J77

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

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