Applying Runge-Kutta method to circular motion

[Scipio]

Hey People!

I'm trying to approximate circular motion applying the Runge-Kutta method. I use the following functions as my derivatives for the velocities vel_x and vel_y:

double accx(double x, double y,double vel_x, double vel_y)
{
  double vv = vel_x*vel_x + vel_y*vel_y;
  double r = sqrt(x*x + y*y);
  double acc = vv/r;
  return acc * -1 * cos(angle(x,y));
}

double accy(double x, double y, double vel_x, double vel_y)
{
  double vv = vel_x*vel_x + vel_y*vel_y;
  double r = sqrt(x*x + y*y);
  double acc =  vv/r;
  return acc*-1 * sin(angle(x,y));
}

And here I perform an iteration:

 double kx[4];
      double ky[4];
      double tempx;
      double tempy;

      //K0
      kx[0] = accx(x,y,vel_x,vel_y);
      ky[0] = accy(x,y,vel_x,vel_y);

      //K1
      tempx = x + dt/2*(vel_x+dt/2*kx[0]);
      tempy = y + dt/2*(vel_y+dt/2*ky[0]);
      kx[1] = accx(tempx,tempy,vel_x + dt/2*kx[0],vel_y+dt/2*ky[0]);
      ky[1] = accy(tempx,tempy,vel_x + dt/2*kx[0],vel_y+dt/2*ky[0]);

      //K2
      tempx = x + dt/2*(vel_x+dt/2*kx[1]);
      tempy = y + dt/2*(vel_y+dt/2*ky[1]);
      kx[2] = accx(tempx,tempy,vel_x + dt/2*kx[1],vel_y+dt/2*ky[1]);
      ky[2] = accy(tempx,tempy,vel_x + dt/2*kx[1],vel_y+dt/2*ky[1]);

      //K4
      tempx = x + dt*(vel_x+dt*kx[2]);
      tempy = y + dt*(vel_y+dt*ky[2]);
      kx[3] = accx(tempx,tempy,vel_x + dt*kx[2]  ,vel_y+dt*ky[2]);
      ky[3] = accy(tempx,tempy,vel_x + dt*kx[2]  ,vel_y+dt*ky[2]);


      vel_x += dt/6*(kx[0]+2*kx[1]+2*kx[2]+kx[3]);
      vel_y += dt/6*(ky[0]+2*ky[1]+2*ky[2]+ky[3]);
      
      x+=dt*vel_x;
      y+=dt*vel_y;

However, if I analyse the results, I still get a diverging circle. Is it possible to make an accurate approximation using this method? If it is, what am I doing wrong?

Thanks!

[Scipio]

Hey people,

For anyone interested: I figured it out. Problem is that you need to apply Runge - Kutta to both the velocity and position. This can be done by using a class that holds all the information on a certain 'state', and as such the method can be generalized to any problem.

Cheers