The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Lie-group methods
Abstract
Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively correct geometry and dynamics and in the minimization of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, highlighting theory, algorithmic issues and a number of applications.
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Cites
Harary, F. (1969) · Cited by 10,739
Mathematical Methods of Classical Mechanics
Arnold, V. I. (1989) · Graduate Texts in Mathematics · doi:10.1007/978-1-4757-2063-1 · Cited by 9,116
Handbook of Mathematical Functions
(2018) · A Century of Excellence in MEASUREMENTS, STANDARDS, and TECHNOLOGY · doi:10.1201/9781351069397-39 · Cited by 9,062
Solving ordinary differential equations I. nonstiff problems
(1987) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(87)90083-8 · Cited by 4,077
Numerical Initial Value Problems in Ordinary Differential Equations
I., E., & Gear, C. W. (1973) · Mathematics of Computation · doi:10.2307/2005674 · Cited by 3,926
Numerical Initial Value Problems in Ordinary Differential Equations
Watt, J. M. (1972) · The Computer Journal · doi:10.1093/comjnl/15.2.155 · Cited by 3,518
Abraham, R., & Young, H. D. (1968) · American Journal of Physics · doi:10.1119/1.1974504 · Cited by 3,086
Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
Marsden, J. E., & Ratiu, T. S. (1999) · Texts in Applied Mathematics · doi:10.1007/978-0-387-21792-5 · Cited by 2,961
Methods of Numerical Integration.
S., F., Davis, P. J., & Rabinowitz, P. (1986) · Mathematics of Computation · doi:10.2307/2008014 · Cited by 2,735
On the exponential solution of differential equations for a linear operator
Magnus, W. (1954) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160070404 · Cited by 2,433
Cited by
The Magnus expansion and some of its applications
Blanes, S., Casas, F., Oteo, J. A., & Ros, J. (2009) · Physics Reports · doi:10.1016/j.physrep.2008.11.001 · Cited by 1,157
Regularizing Flows for Constrained Matrix-Valued Images
Chefd'hotel, C., Tschumperlé, D., Deriche, R., & Faugeras, O. (2004) · Journal of Mathematical Imaging and Vision · doi:10.1023/b:jmiv.0000011920.58935.9c · Cited by 648
From 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
Metadata
- Authors
- Iserles, A., Munthe-Kaas, H. Z., Nørsett, S. P., & Zanna, A.
- Venue
- Acta Numerica
- Publisher
- Cambridge University Press (CUP)
- Published
- 2000-01
- Volume
- 9
- Pages
- 215-365
- ISSN
- 0962-4929 (ISSN-L)
- 1474-0508
- OpenAlex
- W2061356302
- Cited by
- 782
- References
- 28
- FWCI
- 28.92
- Type
- journal article
- Language
- en
- Open access
- closed
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- Iserles, A., Munthe-Kaas, H. Z., Nørsett, S. P., & Zanna, A. (2000). Lie-group methods. Acta Numerica. https://doi.org/10.1017/s0962492900002154
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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