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Article

Pozza, Stefano ; Van Buggenhout, Niel
The $\star$-product approach for linear ODEs: A numerical study of the scalar case. (English). In: Chleboun, J., Kůs, P., Papež, J., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Jablonec nad Nisou, June 19-24, 2022. Institute of Mathematics CAS, Prague, 2023. pp. 187-198
MSC: 34A25, 65L05, 94A11 | DOI: 10.21136/panm.2022.17
Keywords:
ordinary differential equations; Volterra composition; Legendre polynomials
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.
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