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I need to solve a system of stiff ODE's using the RK4 method. I know how to solve a single ODE but am struggling with the concept of how to do a system. The equations are as follows: $\frac{dy_1}{dt}=-0.013y_1-10000y_1y_3$

$\frac{dy_2}{dt}=-2500y_2y_3$

$\frac{dy_3}{dt}=-0.013y_1-1000y_1y_3-2500y_2y_3$

Where: $ y_1(0)=1$, $ y_2(0)=1$, $ y_3(0)=0$

I don't need help programming, just some general advice about how to even set this problem up would be great.

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The specifics depend on the programming language.

You implement the RK4 methods so that all y and k are or can be vectors.

Then you implement the ODE function to be used in the RK4 method as

vector dydt = odefunc(real x, vector y)
    dydt[1] =−0.013*y[1]−10000*y[1]*y[3]
    dydt[2]=−2500*y[2]*y[3]
    dydt[3]=−0.013*y[1]−1000*y[1]*y[3]−2500*y[2]*y[3]
    return dydt
 end

and call

t0=0
tf=???
y0=vector([1,1,0])
yf = rk4(odefunc, t0,y0,tf,h)
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