Antonella Zanna November 12, 1998  Home/Search
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Abstract: We introduce a symmetric version of the Fer expansion for the solution of the ODE y fl(t; y)y. We show that the scheme are time symmetric for linear problems, and, because of the symmetry of the scheme, one gets order 2p + 2 whereby the classical Fer expansion would display order 2p + 1 only. This reduces significantly the computational cost of the classical Fer expansion. We prove the convergence of the proposed symmetric schemes and obtain an estimate of the radius of convergence. We... (Update)
Context of citations to this paper: More
.... higher order Gaussian type methods are not time symmetric for nonlinear problem is also easily verified by numerical experiments (see for instance [25]) 1.2 Time symmetry of Lie group implicit midpoint Let us return to the Lie group implicit midpoint scheme (1:5) We can...
.... the use of the Fer and Magnus expansions for numerically solving differential equations has been investigated by a number of people [15, 16, 17, 27, 36]. 27] discusses the use of graded Lie algebras and implementation issues for deriving Lie bracket identities in...
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BibTeX entry: (Update)
A. Zanna. The Fer expansion and time symmetry: a Strang-type approach. Technical Report NA1998/14, DAMTP, 1998. http://citeseer.ist.psu.edu/zanna98fer.html More
@article{ zanna01fer,
author = "Antonella Zanna",
title = "The {Fer} expansion and time-symmetry: {A Strang}-type approach",
journal = "Applied Numerical Mathematics: Transactions of IMACS",
volume = "39",
number = "3--4",
pages = "435--459",
year = "2001",
url = "citeseer.ist.psu.edu/zanna98fer.html" }
Citations (may not include all citations):1120 Handbook of Mathematical Functions (context) - Abramowitz, Stegun - 1965
229 Solving Ordinary Differential Equations (context) - Hairer, Nrsett et al. - 1993
191 Solving Ordinary Differential Equations II (context) - Hairer, Wanner - 1991
52 Numerical Hamiltonian Problems (context) - Sanz-Serna, Calvo - 1994
25 Approximating the exponential from a Lie algebra to a Lie gr.. (context) - Celledoni, Iserles
25 Collocation and relaxed collocation for the Fer and the Magn.. (context) - Zanna
19 Solving Linear Ordinary Differential Equations by Exponentia.. (context) - Iserles - 1984
17 An Introduction to Lie Groups and Symplectic Geometry (context) - Bryant - 1995
17 High Order Runge--Kutta Methods on Manifolds (context) - Munthe-Kaas
17 Runge--Kutta Methods on Lie Groups (context) - Munthe-Kaas - 1998
13 the Numerical Solution of Isospectral Flows (context) - Zanna - 1998
12 Magnus and Fer expansion for matrix differential equations: .. (context) - Oteo, Blanes et al. - 1998
11 Computations in a free Lie algebra (context) - Munthe-Kaas, Owren - 1998
6 the solution of differential equations in Lie groups (context) - Iserles, Nrsett
6 pU par produit infini d'exponentielles matricielles (context) - Fer, equation - 1958
5 Lie algebraic solution of linear differential equations (context) - Wei, Norman - 1963
4 Approximately preserving symmetries in numerical integration (context) - Iserles, McLachlan et al.
3 Efficient approximantion of Sturm--Liouville problems using .. (context) - Moan
3 the reversibility of the canonical magnus expansion (context) - Iserles, Nrsett et al.
1 Lie-group methods and symplecticity (context) - Eng, Munthe-Kaas et al.
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