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.

翻译：本文提出一种结合半径多项式方法与Haar小波的微分方程后验误差估计算法框架。通过采用Haar小波，我们获得了微分算子与二次非线性项矩阵表示的递归结构，这种结构可被半径多项式方法利用以获取$L^2$意义下的误差估计。这使得该方法能适用于系统或解不连续的情形，而这是其他基于半径多项式方法的局限性。数值算例展示了该方法的实际实现过程。