# differential equations – NDSolve with non local boundary condition

I’m interested in solving the 1D time-dependent Schrodinger equation $$i partial_t u(x,t) = -partial_x^2 u(x,t) + V(x,t) u(x,t)$$ with a transparent boundary condition at, for instance, $$x = x_0$$ :
$$partial_x u(x_0,t) propto e^{-i V t} frac{d}{dt} int_0^t frac{u(x_0,tau) e^{i V tau}}{sqrt{t-tau}} d tau$$
which is non-local in the variable $$t$$.

I was not able to implement that boundary condition “as is” into `NDSolve()`

Is there a way to use that non-local boundary condition with `NDSolve()` ?