Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 57 min ago
PreprintarXiv licencearXiv

Asymptotic-Preserving Exponential Integrators applied to the Hyperbolic Korteweg-de Vries System

  • Abhijit Biswas
  • Sebastiano Boscarino
  • David I. Ketcheson
  • Giovanni Russo
Open at sourcePDFDOICite

Abstract

We study the application of exponential time integration methods, coupled with Fourier pseudospectral space discretization, to the hyperbolic Korteweg-de Vries (KdVH) system. We investigate the asymptotic preserving (AP) properties of such discretizations, showing that, in general, Lawson methods are not asymptotic preserving, because the auxiliary (derivative-approximating) variables do not satisfy the limit equilibrium manifold, whereas exponential time differencing (ETD) methods are AP for all components, including both the solution variable and the auxiliary variables. We also present an efficient numerical implementation based on an exact formula for the matrix exponential of this system, and compare it with previously-proposed ImEx Runge-Kutta time integration, showing that exponential methods can be competitive in this context.

Related

  1. Asymptotic preserving IMEX Active Flux schemes for a hyperbolic approximation of the Korteweg-de Vries equation
    Simon Krotsch, Wasilij Barsukow, Christian Klingenberg
    arXivPreprintCC BY-NC-SA 4.0Full textNumerical analysis & scientific computingarXiv
  2. An asymptotic-and curl-preserving finite volume scheme for a novel hyperbolic barotropic Navier-Stokes model
    Antoine Guines, Walter Boscheri, Sergey Gavrilyuk +1
    HALPreprintCC BY-NC-ND 4.0Full textGeneral mathematicsHAL
  3. Analysis of split exponential integrators for semilinear problems with noncommuting operators
    Luca Battestini, Marco Caliari, Fabio Cassini
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Self-consistent flow maps based on commutator-free exponential integrators
    Xiaofeng Cai, Linghui Kong
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingPlasma physicsarXiv
  5. Boris-type exponential integrators for charged-particle dynamics in strong magnetic fields
    Marlis Hochbruck, Sebastian Merk
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{biswas2026asymptoticpreserving,
  title = {{Asymptotic-Preserving Exponential Integrators applied to the Hyperbolic Korteweg-de Vries System}},
  author = {Abhijit Biswas and Sebastiano Boscarino and David I. Ketcheson and Giovanni Russo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22864},
  eprint = {2609.22864},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22864},
}
RIS
TY  - UNPB
TI  - Asymptotic-Preserving Exponential Integrators applied to the Hyperbolic Korteweg-de Vries System
AU  - Abhijit Biswas
AU  - Sebastiano Boscarino
AU  - David I. Ketcheson
AU  - Giovanni Russo
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22864
UR  - https://arxiv.org/abs/2609.22864
AB  - We study the application of exponential time integration methods, coupled with Fourier pseudospectral space discretization, to the hyperbolic Korteweg-de Vries (KdVH) system. We investigate the asymptotic preserving (AP) properties of such discretizations, showing that, in general, Lawson methods are not asymptotic preserving, because the auxiliary (derivative-approximating) variables do not satisfy the limit equilibrium manifold, whereas exponential time differencing (ETD) methods are AP for all components, including both the solution variable and the auxiliary variables. We also present an efficient numerical implementation based on an exact formula for the matrix exponential of this system, and compare it with previously-proposed ImEx Runge-Kutta time integration, showing that exponential methods can be competitive in this context.
ER  -