  We consider the dispersion managed nonlinear Schr\"odinger equation with
power-law nonlinearity and its discrete version of equations with step size
$h\in(0,1]$. We prove that the solutions of the discrete equations strongly
converge in $L^2(\mathbb{R})$ to the solution of the dispersion managed NLS as
$h\to 0$ after showing the global well-posedness of the discrete equations.
