Low-storage exponentially fitted explicit Runge-Kutta methods

Higueras, I. ; Montijano, J.I. (Universidad de Zaragoza) ; Rández, L. (Universidad de Zaragoza)

Resumen: In this paper, we study explicit Runge-Kutta (RK) methods for solving high-dimensional systems of ordinary differential equations (ODEs), with oscillatory or periodic solutions, that can be implemented with a few memory registers. We will refer to these schemes as Low-Storage Exponentially Fitted explicit Runge-Kutta methods (LSEFRK).
In order to obtain them, we first study second-order and third-order low-storage (LS) schemes that can be implemented with two memory registers per step of the van der Houwen- and Williamson-type. Next, we construct optimal LSEFRK methods by imposing exponential fitting conditions along with accuracy and stability properties. In this way, new optimal three-stage third-order and five-stage fourth-order LSEFRK schemes are constructed for each type of LS method.
The performance of these new schemes is tested by solving some high-dimensional differential systems with periodic solutions. Comparison with other non-LS exponentially fitted and low-storage non-EF RK methods from the literature shows that the new LSEFRK schemes outperform the efficiency of RK methods that only satisfy either the LS or the EF condition.

Idioma: Inglés

DOI: 10.1016/j.apnum.2025.06.017

Año: 2025

Publicado en: APPLIED NUMERICAL MATHEMATICS 217 (2025), 372-389
ISSN: 0168-9274

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)