Right Runge Kutta 4th method approach?

Question

I have this runge kutta code. However, one mentioned my approach is wrong. And I couldn't really understand why from him, so anyone here, who could give a hint on why this way is wrong?

    Vector3d r = P.GetAcceleration();

    Vector3d s = P.GetAcceleration() + 0.5*m_dDeltaT*r;

    Vector3d t = P.GetAcceleration() + 0.5*m_dDeltaT*s;

    Vector3d u = P.GetAcceleration() + m_dDeltaT*t;

    P.Velocity += m_dDeltaT * (r + 2.0 * (s + t) + u) / 6.0);

====EDIT====

Vector3d are storing the coordinates, x, y, z.

The GetAcceleration returns the acceleration for each x, y, and z.

Answer 1

You have some acceleration function

a(p,q) where p=(x,y,z) and q=(vx,vy,vz)

Your order 1 system that can be solved via RK4 is

dotp = q
dotq = a(p,q)

The stages of the RK method involve an offset of the state vector(s)

k1p = q
k1q = a(p,q)

p1 = p + 0.5*dt*k1p
q1 = q + 0.5*dt*k1q
k2p = q1
k2q = a(p1,q1)

p2 = p + 0.5*dt*k2p
q2 = p + 0.5*dt*k2q
k3p = q2
k3q = a(p2,q2)

etc. You can either adjust the state vectors of the point P for each step, saving the original coordinates, or use a temporary copy of P to compute k2, k3, k4.