Efficient computation of the sinc matrix function for the integration of second-order differential equations

Autor: Aceto, Lidia, Durastante, Fabio
Rok vydání: 2023
Předmět:
Zdroj: Adv Comput Math 50, 109 (2024)
Druh dokumentu: Working Paper
DOI: 10.1007/s10444-024-10202-y
Popis: This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit (pronounced or highly) oscillatory behavior, standard numerical methods are known to perform poorly. Our approach consists in directly discretizing the problem by means of Gautschi-type integrators based on $\operatorname{sinc}$ matrix functions. The novelty contained here is that of using a suitable rational approximation formula for the $\operatorname{sinc}$ matrix function to apply a rational Krylov-like approximation method with suitable choices of poles. In particular, we discuss the application of the whole strategy to a finite element discretization of the wave equation.
Databáze: arXiv