/*  this is a Runge-Kutta integrator of the differential equation 
    y'=F(t,y) where y is a DIM dimensional vector.       */


void runge_kutta_step(t, y, dt)
float t, *y, dt;

{


float  F();

  float k1[DIM], k2[DIM], k3[DIM], k4[DIM], y1[DIM], y2[DIM], y3[DIM];
  int i;
  

  for(i = 0; i < DIM; i++)
    {k1[i] = dt * F(t, y, i);
     y1[i]  = y[i] + k1[i] / 2.;
   }

  for(i = 0; i < DIM; i++)
    {k2[i] = dt * F(t + dt / 2., y1, i);
     y2[i]  = y[i] + k2[i]/2.;
   }

  for(i = 0; i < DIM; i++)
    {k3[i] = dt * F(t + dt / 2., y2, i);
     y3[i]  = y[i] + k3[i];
   }

  for(i = 0; i < DIM; i++)
    {k4[i] = dt * F(t + dt, y3, i);
     y[i] += ( k1[i] + 2. * k2[i] + 2. * k3[i] + k4[i]) / 6.;
   }
}