The ☆ -product approach for linear ODEs: A numerical study of the scalar case

Pozza, Stefano; Van Buggenhout, Niel

  • Programs and Algorithms of Numerical Mathematics, Publisher: Institute of Mathematics CAS(Prague), page 187-198

Abstract

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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.

How to cite

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Pozza, Stefano, and Van Buggenhout, Niel. "The $\star $-product approach for linear ODEs: A numerical study of the scalar case." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2023. 187-198. <http://eudml.org/doc/299011>.

@inProceedings{Pozza2023,
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 straightforwardly extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the method's efficacy and properties in the scalar case.},
author = {Pozza, Stefano, Van Buggenhout, Niel},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {ordinary differential equations; Volterra composition; Legendre polynomials},
location = {Prague},
pages = {187-198},
publisher = {Institute of Mathematics CAS},
title = {The $\star $-product approach for linear ODEs: A numerical study of the scalar case},
url = {http://eudml.org/doc/299011},
year = {2023},
}

TY - CLSWK
AU - Pozza, Stefano
AU - Van Buggenhout, Niel
TI - The $\star $-product approach for linear ODEs: A numerical study of the scalar case
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 187
EP - 198
AB - 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.
KW - ordinary differential equations; Volterra composition; Legendre polynomials
UR - http://eudml.org/doc/299011
ER -

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