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Title: The $\star$-product approach for linear ODEs: A numerical study of the scalar case (English)
Author: Pozza, Stefano
Author: Van Buggenhout, Niel
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Jablonec nad Nisou, June 19-24, 2022
Issue: 2022
Pages: 187-198
Category: math
Summary: 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 straightforwardly extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the method's efficacy and properties in the scalar case. (English)
Keyword: ordinary differential equations
Keyword: Volterra composition
Keyword: Legendre polynomials
MSC: 34A25
MSC: 65L05
MSC: 94A11
DOI: 10.21136/panm.2022.17
Date available: 2023-04-13T06:27:02Z
Last updated: 2023-06-05
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