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.

What is `Vector3d` and what does `GetAcceleration` returns? – The Apache Nov 16 '15 at 17:42 — The Apache, Nov 16 '15 at 17:42
Sorry. I should have went into more details. – user2180833 Nov 16 '15 at 17:46 — user2180833, Nov 16 '15 at 17:46

score 1 · Accepted Answer · answered Nov 16 '15 at 18:59

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.

score 0 · Answer 2 · answered Nov 16 '15 at 17:56

You haven't defined your methods, but the thing that's jumping out at me is you're mixing your results with your inputs. Since Runge-Kutta is a method for calculating y_(n+1) = y_n + hsum(b_ik_i), I would expect your solution to keep your _n terms on the right, and your (n+1) terms on the left. This is NOT what you're doing. Instead, s(n+1) is dependent on r_(n+1) instead of on r_n, t_(n+1) on s_(n+1), and so on. This smells of an error where you attempted to limit the number of variables being used.

With that in mind, can you indicate the actual intermediate values of the calculations your program generates and compare them with the intended intermediate values?

Right Runge Kutta 4th method approach?

2 Answers2