The *-product approach for linear ODEs: a numerical study of the scalar case

2022/09/27 by Stefano Pozza, Pozza, Stefano, Niel Van Buggenhout +1 · 1 citation
Engineering · Mathematics · #34A25 #65L05 #94A11 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2209.13322

openalex publication_date 2022/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the main ideas at the core of this approach in the simpler setting of a scalar ODE. Understanding the scalar case is fundamental since the method can be easily extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the method's efficacy and its properties in the scalar case.

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