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

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 numeri...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 50; no. 6
Main Authors Aceto, Lidia, Durastante, Fabio
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.12.2024
Subjects
Approximation
Discretization
Mathematical analysis
Numerical methods
Partial differential equations
Wave equations
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Summary: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 sinc matrix functions. The novelty contained here is that of using a suitable rational approximation formula for the 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.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10202-y