2023/04/27 by Guilherme Nakassima, Nakassima, Guilherme, Marcio Gameiro +1
Computer Science · Mathematics · #34A34 #34L30 #65G20 #65H10 #65T60 #Digital Filter Design and Implementation #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2304.14536
openalex publication_date 2023/04/27 · openalex created_date 2023/05/02 · openalex updated_date 2026/07/29
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 L2 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.