# NDSolve coupled ode

1. Sep 4, 2015

### bayan

Hi, I need to solve 3 coupled first order ODE's using NDSolve (numerical solution).

This is the code I have used ;

NDSolve[{u'[t] == ((1 - (u[t]/t^2))/(-3 - (u[t]/t^2) - (v[t]/t^2))),
v'[t] == (((u[t]/t^2) - (v[t]/t^2))/(-3 - (u[t]/t^2) - (v[t]/t^2))),
w'[t] == (v[t])/(-3 t^2 - (u[t]) - (v[t])),
u[0] == 0., v[0] == 0., w[0] == 0.}, {u, v, w}, {t, 0.1, 1}]

where u,v and w are functions of t and at t=0, u=v=w=0. However I am getting the following error "Infinite expression 1/0.^2 encountered", but I can't see where the division by zero occurs. Originally t was from 0 to 1, but I tried making it from 0.1 to 1 to ensure no division by zero's were taking place.

Any ideas on how to fix the code? or an alternative way of solving these ode?

Regards

2. Sep 4, 2015

### BvU

I don't see anything wrong, sorry. Even tried to solve:
Code (Text):

u as realvariable (initial, 0)  ;
v as realvariable (initial, 0)  ;
w as realvariable (initial, 0)  ;

eps as realparameter (1e-5)  ;
t as realvariable (eps)  ;

t = time + eps  ;

$u = ((1 - (u/t^2))/(-3 - (u/t^2) - (v/t^2))) ;$v = (((u/t^2) - (v/t^2))/(-3 - (u/t^2) - (v/t^2)))  ;
$w = (v)/(-3*t^2 - (u) - (v)) ; (the$ stands for a time derivative in this simulator)
and that worked:

3. Sep 4, 2015

### bayan

Did NDSolve with the options given work for you? or do you recommend the use of another software to solve those odes?

btw is that code for mathematica?

Regards

4. Sep 4, 2015

### BvU

I don't know where NDSolve lives ? Ah, I googlesee: in MatLab. Don't have that at my disposition.

I abused a chemical flowsheeting program as equation solver, just to see if I would get the same problem as you. Apparently not.