A Numerical Scheme for Harmonic Stochastic Oscillators Based on Asymptotic Expansions

Carmela Scalone ()
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Carmela Scalone: Department of Engineering and Computer Science and Mathematics, University of L’Aquila, 67100 L’Aquila, Italy

Mathematics, 2022, vol. 10, issue 17, 1-9

Abstract: In this work, we provide a numerical method for discretizing linear stochastic oscillators with high constant frequencies driven by a nonlinear time-varying force and a random force. The presented method is constructed by starting from the variation of constants formula, in which highly oscillating integrals appear. To provide a suited discretisation of this type of integrals, we propose quadrature rules based on asymptotic expansions. Theoretical considerations and numerical experiments comparing the method with a standard approach on physical models are introduced.

Keywords: stochastic oscillators; numerical method; asymptotic expansions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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