Skip to content
DraconiticResearch
Search Sources API
182,549 studies31 sourcesUpdated 6 min ago
PreprintarXiv licencearXiv

Analysis of split exponential integrators for semilinear problems with noncommuting operators

  • Luca Battestini
  • Marco Caliari
  • Fabio Cassini
Open at sourcePDFDOICite

Abstract

Splitting the exponential and exponential-like functions can significantly reduce the overall computational cost of exponential integrators, providing a strong motivation for their rigorous analysis. In this paper, we analyze splitting errors for two noncommuting unbounded operators and derive new representations that include the popular Lie--Trotter and Strang cases. Moreover, within the abstract framework of strongly continuous semigroups, we prove the convergence of a split version of the exponential Euler method and a second-order exponential Runge--Kutta method for semilinear problems. Numerical experiments on a nonlinear dispersive equation and a diffusion--reaction equation demonstrate the theoretical findings, stability properties, and efficiency of the proposed split exponential integrators compared to the state of the art.

Related

  1. Asymptotic-Preserving Exponential Integrators applied to the Hyperbolic Korteweg-de Vries System
    Abhijit Biswas, Sebastiano Boscarino, David I. Ketcheson +1
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  2. Self-consistent flow maps based on commutator-free exponential integrators
    Xiaofeng Cai, Linghui Kong
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingPlasma physicsarXiv
  3. Boris-type exponential integrators for charged-particle dynamics in strong magnetic fields
    Marlis Hochbruck, Sebastian Merk
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field
    Lina Wang, Bin Wang, Beibei Zhu
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  5. Entropy instability and rigidity for the exponential semilinear heat equation
    Yuxia Guo, Jionghao Lv
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{battestini2026analysis,
  title = {{Analysis of split exponential integrators for semilinear problems with noncommuting operators}},
  author = {Luca Battestini and Marco Caliari and Fabio Cassini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07989},
  eprint = {2610.07989},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07989},
}
RIS
TY  - UNPB
TI  - Analysis of split exponential integrators for semilinear problems with noncommuting operators
AU  - Luca Battestini
AU  - Marco Caliari
AU  - Fabio Cassini
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.07989
UR  - https://arxiv.org/abs/2610.07989
AB  - Splitting the exponential and exponential-like functions can significantly reduce the overall computational cost of exponential integrators, providing a strong motivation for their rigorous analysis. In this paper, we analyze splitting errors for two noncommuting unbounded operators and derive new representations that include the popular Lie--Trotter and Strang cases. Moreover, within the abstract framework of strongly continuous semigroups, we prove the convergence of a split version of the exponential Euler method and a second-order exponential Runge--Kutta method for semilinear problems. Numerical experiments on a nonlinear dispersive equation and a diffusion--reaction equation demonstrate the theoretical findings, stability properties, and efficiency of the proposed split exponential integrators compared to the state of the art.
ER  -