  This work presents a framework for a-posteriori error-estimating algorithms
for differential equations which combines the radii polynomial approach with
Haar wavelets. By using Haar wavelets, we obtain recursive structures for the
matrix representations of the differential operators and quadratic
nonlinearities, which can be exploited for the radii polynomial method in order
to get error estimates in the $L^2$ sense. This allows the method to be
applicable when the system or solution is not continuous, which is a limitation
of other radii-polynomial-based methods. Numerical examples show how the method
is implemented in practice.
