Email this article Asymptotic Solutions of the Cauchy Problem with Localized Initial Data for a Finite-Difference Scheme Corresponding to the One-Dimensional Wave Equation
- Authors: Sergeev S.A.1,2
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Affiliations:
- Ishlinsky Institute for Problems in Mechanics RAS
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 106, No 5-6 (2019)
- Pages: 800-813
- Section: Article
- URL: https://journal-vniispk.ru/0001-4346/article/view/151866
- DOI: https://doi.org/10.1134/S0001434619110130
- ID: 151866
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Abstract
We pose the Cauchy problem with localized initial data that arises when passing from an explicit difference scheme for the wave equation to a pseudodifferential equation. The solution of the Cauchy problem for the difference scheme is compared with the asymptotics of the solution of the Cauchy problem for the pseudodifferential equation. We give a detailed study of the behavior of the asymptotic solution in the vicinity of the leading edge, where yet another version of the asymptotic solution is constructed based on vertical manifolds.
About the authors
S. A. Sergeev
Ishlinsky Institute for Problems in Mechanics RAS; Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: sergeevse1@yandex.ru
Russian Federation, Moscow, 119526; Dolgoprudnyi, Moscow Oblast, 141701
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