% Takes one time step of size dt using the rungekutta method
% starting from v_0 and where the function F(v,t) gives the
% time derivatives.
function v = rungekutta_4(v, t , dt, F)
    k1 = F(v         ,t      );
    k2 = F(v+0.5*dt*k1,t+0.5*dt);
    k3 = F(v+0.5*dt*k2,t+0.5*dt);
    k4 = F(v+    dt*k3,t+    dt);
    v = v + (1/6)*(k1+2*(k2+k3)+k4)*dt;
end