Best polynomial approximation for non-autonomous linear ODEs in the $\star$-product framework

TL;DR

This paper introduces a novel approach using the $igstar$-product framework for optimal polynomial approximation of solutions to linear non-autonomous ODEs, providing theoretical error bounds and new solution methods.

Contribution

It is the first to formulate polynomial approximation of non-autonomous linear ODEs within the $igstar$-product framework, advancing analytical and numerical solution techniques.

Findings

Derived upper bounds for approximation error.

Established a formal problem statement in the $igstar$-product framework.

Presented new approaches for solving non-autonomous linear ODEs.

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 $\star$-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.