Second-order differential equation using the C ++ Boost odeint library

Question

Using the boost C ++ odeint library, is it possible to solve a second-order differential equation defined as follows:

m*x''[i] + x'[i] = K*\sum{j=1,N} sin(x[j] - x[i]), where i = 1,2,3..N.
m = 1, K = 1

where the initial value of x is a vector or an array of N uniformly generated random numbers from 0 to 2 * pi. I want to integrate the above equation with runge_kutta stepper odeint?

I can solve this by writing the above equation. in two differential equations of the first order, but then in this case, how will the odeint pedometer be written or modified?

Answer 1

ODE 2 N. N x[i], N x'[i]

void ode( state_type const& x , state_type &dxdt , double t )
{
    for( size_t i=0 ; i<N ; ++i )
    {
        double sum = 0.0;
        // calculate sum
        dxdt[i] = x[i+N];
        dxdt[i+N] = K * sum;
    }
}

size_t N = 512;
typedef std::vector< double > state_type;
state_type x( 2 * N );
// initialize x
double t_start = 0.0 , t_end = 10.0 , dt = 0.01;
odeint::integrate( ode , x , t_start , t_end , dt );