The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Exponential integrators
Open accessAbstract
In this paper we consider the construction, analysis, implementation and application of exponential integrators. The focus will be on two types of stiff problems. The first one is characterized by a Jacobian that possesses eigenvalues with large negative real parts. Parabolic partial differential equations and their spatial discretization are typical examples. The second class consists of highly oscillatory problems with purely imaginary eigenvalues of large modulus. Apart from motivating the construction of exponential integrators for various classes of problems, our main intention in this article is to present the mathematics behind these methods. We will derive error bounds that are independent of stiffness or highest frequencies in the system. Since the implementation of exponential integrators requires the evaluation of the product of a matrix function with a vector, we will briefly discuss some possible approaches as well. The paper concludes with some applications, in which exponential integrators are used.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
Moler, C., & Van Loan, C. (2003) · SIAM Review · doi:10.1137/s00361445024180 · Cited by 2,357
Functions of Matrices: Theory and Computation
Higham, N. J. (2008) · doi:10.1137/1.9780898717778 · Cited by 2,113
On Krylov Subspace Approximations to the Matrix Exponential Operator
Hochbruck, M., & Lubich, C. (1997) · SIAM Journal on Numerical Analysis · doi:10.1137/s0036142995280572 · Cited by 795
Self-citationFrom Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis
Lubich, C. (2008) · Zurich Lectures in Advanced Mathematics · doi:10.4171/067 · Cited by 366
Cited by
Du, Q., Ju, L., Li, X., & Qiao, Z. (2021) · SIAM Review · doi:10.1137/19m1243750 · Cited by 294
Time Integration of Tensor Trains
Lubich, C., Oseledets, I. V., & Vandereycken, B. (2015) · SIAM Journal on Numerical Analysis · doi:10.1137/140976546 · Cited by 183
Metadata
- Authors
- Hochbruck, M., & Ostermann, A.
- Venue
- Acta Numerica
- Publisher
- Cambridge University Press (CUP)
- Published
- 2010-05
- Volume
- 19
- Pages
- 209-286
- ISSN
- 0962-4929 (ISSN-L)
- 1474-0508
- OpenAlex
- W4211077197
- Cited by
- 1,061
- References
- 4
- FWCI
- 27.19
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Exponential integrators. https://app.cochat.ai/papers/10.1017/s0962492910000048
- The paper
- Hochbruck, M., & Ostermann, A. (2010). Exponential integrators. Acta Numerica. https://doi.org/10.1017/s0962492910000048
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
