Best polynomial approximation for non-autonomous linear ODEs in the ⋆-product framework

2024/04/30 by Stefano Pozza, Pozza, Stefano
Mathematics · #37C60 #46F10 #65L05 #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2404.19645

openalex publication_date 2024/04/30 · openalex created_date 2024/05/03 · openalex updated_date 2026/08/01

Abstract

We present the first formulation of the optimal polynomial approximation of the solution of linear non-autonomous systems of ODEs in the framework of the so-called ⋆-product. This product is the basis of new approaches for the solution of such ODEs, both in the analytical and the numerical sense. The paper shows how to formally state the problem and derives upper bounds for its error.

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