Runge Kutta 3 ODE

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?

Answer 1

[Alan Stevens]

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!