# Approximating System of ODE's

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1. Oct 28, 2015

### worryingchem

My question is about whether it's possible to use the Euler Forward or 4th order Runge-Kutta Methods to approximate the following system ( where the differential of other equations are on the right hand side) :
$$\begin{cases} \frac{dy_1}{dt} = f_1(y_1,y_2,y'_2, ... , y_n, y'_n, t) \\ \frac{dy_2}{dt} = f_2(y_1,y'_1,y_2, ... , y_n, y'_n, t) \\ ...\\ \frac{dy_n}{dt} = f_n(y_1,y'_1, ... , y_{n-1}, y'_{n-1}, y_n, t) \\ \end{cases}$$
I know you can do it for the normal form: $\frac{d^{(n)}y}{dt^{(n)}} = f(y, y', y'', ... , y^{(n)}, t)$ and it's also possible to analytically solve differential equations of that form using linear algebra, but I'm not sure when it's not in the normal form.

2. Oct 28, 2015

### bigfooted

Yes, you can use those schemes because you know and use all the quantities at the right hand side at timestep 't'. However, it will be difficult to determine the stability criterion for the timestep to use a priori.

3. Oct 29, 2015

### worryingchem

Thank you, I forgot about the initial values used to approximate this.