# Runge Kutta 3 ODE

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Hugo B on 4 Feb 2022
Answered: Alan Stevens on 4 Feb 2022
Part of bigger project. The task:
4. Implement the Runge-Kutta-3 (RK3) solver in Matlab and use it to compute the time evolution of the positions of the three bodies. For an ODE in general form y 0 = f(t, y) the RK3 method is defined as follows:
K1 = hf(ti , yi)
K2 = hf(ti + 1 2 h, yi + 1 2K1)
K3 = hf(ti + h, yi − K1 + 2K2)
yi+1 = yi + 1 6 (K1 + 4K2 + K3) where ti = t0 + ih.
As the name suggests, it is of third order accuracy.
Our code so far:
for i=1:n
t(i)=t(0)+i*h;
K1=h*f(t(i),y(i));
K2=h*f(t(i)+h/2,y(i)+K1/2);
K3=h*f(t(i)+h,y(i)-K1+2*K2);
y(i+1)=y(i)+(K1+4*K2+K3)/6;
end
We have tried putting n=different numbers but dont know what we are doing.
Error message:
Array indices must be positive integers or logical values.
Error in RK3 (line 7)
t(i)=t(0)+i*h;
What is the problem and how do solve the error?

Alan Stevens on 4 Feb 2022
You can't have
t(i)=t(0)+i*h;
indices must be a positive integer - you have t(0), Matlab doesn't like this!

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