An Unfiltered Low-Regularity Integrator for the KdV Equation with Solutions Below H1.
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| Title: | An Unfiltered Low-Regularity Integrator for the KdV Equation with Solutions Below H1. |
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| Authors: | Li, Buyang1 (AUTHOR) buyang.li@polyu.edu.hk, Wu, Yifei2 (AUTHOR) yerfmath@gmail.com |
| Source: | Foundations of Computational Mathematics. Jun2026, Vol. 26 Issue 3, p1321-1380. 60p. |
| Subjects: | Korteweg-de Vries equation, Time integration scheme, Harmonic analysis (Mathematics), Stability theory, Perturbation theory, Numerical analysis |
| Abstract: | This article is concerned with the construction and analysis of new time discretizations for the KdV equation on a torus for low-regularity solutions below H 1 . New harmonic analysis tools, including averaging approximations to the exponential phase functions and trilinear estimates of the KdV operator, are established for the construction and analysis of time discretizations with higher convergence orders under low-regularity conditions. In addition, new perturbation techniques are introduced to establish stability estimates of time discretizations under low-regularity conditions without using filters when the energy techniques fail. The proposed method is proved to be convergent with order γ (up to a logarithmic factor) in L 2 under the regularity condition u ∈ C ([ 0 , T ] ; H γ) for γ ∈ (0 , 1 ] . [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | This article is concerned with the construction and analysis of new time discretizations for the KdV equation on a torus for low-regularity solutions below H 1 . New harmonic analysis tools, including averaging approximations to the exponential phase functions and trilinear estimates of the KdV operator, are established for the construction and analysis of time discretizations with higher convergence orders under low-regularity conditions. In addition, new perturbation techniques are introduced to establish stability estimates of time discretizations under low-regularity conditions without using filters when the energy techniques fail. The proposed method is proved to be convergent with order γ (up to a logarithmic factor) in L 2 under the regularity condition u ∈ C ([ 0 , T ] ; H γ) for γ ∈ (0 , 1 ] . [ABSTRACT FROM AUTHOR] |
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| ISSN: | 16153375 |
| DOI: | 10.1007/s10208-025-09702-0 |
