Accelero-summation of the formal solutions of nonlinear difference equations

In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of "level 1(+)". Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains; we prove that, under very general conditions, the formal solution is accelero-summable. Its sum is an analytic solution of the equation, represented asymptotically by the formal solution in a certain unbounded domain