Lie-group methods

By Arieh Iserles, H. Munthe-Kaas, Syvert P. Nørsett, A. Zanna. Acta Numerica, 2000

382 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ddb8c0b771d18fc83d4ee698df7dd16a3a2d556f

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In Computational Mechanics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Numerical approach to simulating turbulent flow of a viscoelastic polymer solution (2003, methodology): “For example, a modified version of the Euler scheme based on the Cayley expansion [28] can be written as shown below”
Geometric integrators for ODEs (2006, methodology): “If solutions are confined to lie in the orbit of a group action, each orbit is a homogeneous space and it is possible to make big progress using Lie group integrators [57].”
On the numerical quadrature of highly‐oscillating integrals I: Fourier transforms (2004, methodology): “The secret of the success of ‘standard’ Magnus integrators i s that all underlying multivariate integrals can be computed to high precision very eco nomically, in a small number of function evaluations and reasonable volume of linear algebra ( Iserles et al. 2000 ).”
Adiabatic Integrators for Highly Oscillatory Second-Order Linear Differential Equations with Time-Varying Eigendecomposition (2005, background): “The brackets [·, ·] denote the commutator [X , Y ] = XY Y X. For a numerical treatment, the series is truncated and the integrals are replaced by quadrature approximations; see, e.g., [ 10 ].”
High Order Optimized Geometric Integrators for Linear Differential Equations (2002, methodology): “It has been argued [ 12 ] that one of the reasons which explains the superior performance of Lie-group solvers might be that standard methods invariably employ the ansatz that locally the solution behaves like a polynomial in t ,w hereas the former are based on a representation of the solution as an”