# Coupled first order differential equations

1. Jul 1, 2005

### Rafique Mir

How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.

2. Jul 1, 2005

### abercrombiems02

First you need to write the equations in state vairable form and then convert it to state space format where
xdot = Ax + B A is a matrix, x and B are vectors
y = Cx + Du C is the relationship between x and y, and D is an initial condition

Now just pick a single equation and perform your numerical calculations plug those results into all the others and see what you obtain, doing this by hand really isn't recommended. It far worse than solving a system of 6 ordinary algebraic equations by hand whihc is already quite the task. I suggest running ODE 45 on it in matlab

3. Jul 1, 2005

### saltydog

Here you go dude:

$$\frac{dx_1}{dt}=f_1(t,x_1,x_2,x_3,x_4,x_5,x_6)$$
$$.$$

$$.$$

$$.$$

$$\frac{dx_6}{dt}=f_6(t,x_1,x_2,x_3,x_4,x_5,x_6)$$

Now, each time you increment t, you have to determine the corresponding increments in $x_i$.

You see, it's done in parallel: Increment t, calculate $x_1[/tex] through [itex]x_6$ increment, then increment t again, do all six again, and so fourth to the end.

How about posting the equations?

Last edited: Jul 1, 2005