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Error analysis of multirate leapfrog-type methods for second-order semilinear ODEs

Carle, Constantin; Hochbruck, Marlis

Abstract:

In this paper we consider the numerical solution of second-order semilinear differential equations, for which the stiffness is induced by only a few components of the linear part. For such problems, the leapfrog scheme suffers from severe restrictions on the step size to ensure stability. We thus propose a general class of multirate leapfrog-type methods which allows to use step sizes which are independent on the stiff part of the equation and also very efficient to implement. This class comprises local time-stepping schemes [5, 7] but also locally implicit or locally trigonometric integrators. Our main contribution is a rigorous error and stability analysis with special emphasis on explicit multirate methods, which are based on stabilized leapfrog-Chebyshev polynomials introduced in [4].


Volltext §
DOI: 10.5445/IR/1000133957
Veröffentlicht am 15.06.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 06.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000133957
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 22 S.
Serie CRC 1173 Preprint ; 2021/26
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter time integration, second-order ode, leapfrog method, stability analysis, error analysis, Hamiltonian systems, CFL condition, Chebyshev polynomials, wave equation
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