OK I really don't understand how to use this method of numerical integration.
I have the coupled differential equations:
dx/dt = f(I, I') = dI/dt
df/dt = g(I, I') = -(R/L)f(I, I') - I/(LC)
Now I have a source that says to solve the formulae
dI/dt = Ií and
dIí/dt = f(Ií, I) = -(R/L)Ií Ė I/(LC)
You use tn+1 = tn + h
In+1 = In + (K1 + 2k2 + 2k3 + k4)/6
Iín+1 = Iín + (l1 + 2l2 + 2l3 + l4)/6
where k1 = h x Ií
l1 = h x f(Ií, I)
k2 = h x (Ií + l1/2)
l2 = h x f(Ií + l1/2, I + k1/2)
k3 = h x (Ií + l2/2)
l3 = h x f(Ií + l2/2, I + k2/2)
k4 = h x (Ií + l3)
l4 = h x f(Ií + l3, I + k3)
However I cannot see how these derive from the normal runge kutta formulae for a single differential equation, nor can I see how to apply this to my problem. Finally, once I have solved the initial problem I have to solve
d2I/dt2 + (R/L)dI/dt + I/(LC) = (1/L)dV/dt
Where V = V0cos(wt)
The LHS is the part I need to solve for the first part using runge kutta, having split it into the coupled equations shown at the top.
Plese, please, please help!