Construction and analysis of an explicit fourth-order symmetric low-regularity integrator for the semilinear Klein-Gordon equation
Abstract
In this paper, we propose and analyse a novel explicit fourth-order symmetric low-regularity trigonometric integrator for the semilinear Klein-Gordon equation with non-smooth solution in the d-dimensional space, where d=1,2,3. The integrator is constructed based on the full use of Duhamel's formula, the employment of a twisted function tailored for trigonometric integrals and the symmetrization procedure of trigonometric integrators. Robust error analysis is conducted, demonstrating that the proposed scheme achieves fourth-order accuracy in the energy space under a weak regularity requirement in H2+max(μ,1)(𝕋d)× H1+max(μ,1)(𝕋d) with μ> d/2. A numerical experiment shows that the proposed low-regularity integrator is much more accurate than some well-known exponential integrators for approximating the Klein-Gordon equation with non-smooth solutions.
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BibTeX
@misc{wang2026construction,
title = {{Construction and analysis of an explicit fourth-order symmetric low-regularity integrator for the semilinear Klein-Gordon equation}},
author = {Bin Wang and Zhen Miao and Yaolin Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15397},
eprint = {2610.15397},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15397},
}
RIS
TY - UNPB
TI - Construction and analysis of an explicit fourth-order symmetric low-regularity integrator for the semilinear Klein-Gordon equation
AU - Bin Wang
AU - Zhen Miao
AU - Yaolin Jiang
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15397
UR - https://arxiv.org/abs/2610.15397
AB - In this paper, we propose and analyse a novel explicit fourth-order symmetric low-regularity trigonometric integrator for the semilinear Klein-Gordon equation with non-smooth solution in the d-dimensional space, where d=1,2,3. The integrator is constructed based on the full use of Duhamel's formula, the employment of a twisted function tailored for trigonometric integrals and the symmetrization procedure of trigonometric integrators. Robust error analysis is conducted, demonstrating that the proposed scheme achieves fourth-order accuracy in the energy space under a weak regularity requirement in H^2+max(μ,1)(𝕋^d)× H^1+max(μ,1)(𝕋^d) with μ> d/2. A numerical experiment shows that the proposed low-regularity integrator is much more accurate than some well-known exponential integrators for approximating the Klein-Gordon equation with non-smooth solutions.
ER -