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High Order Optimized Geometric Integrators for Linear Differential Equations |
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| Authors: | S Blanes F Casas J Ros |
| Institution: | (1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, England;(2) Departament de Matemàtiques, Universitat Jaume I, 12071- Castellón, Spain;(3) Departament de Física Teòrica and IFIC, Universitat de València, 46100- Burjassot, Valencia, Spain |
| Abstract: | In this paper new integration algorithms based on the Magnus expansion for linear differential equations up to eighth order are obtained. These methods are optimal with respect to the number of commutators required. Starting from Magnus series, integration schemes based on the Cayley transform an the Fer factorization are also built in terms of univariate integrals. The structure of the exact solution is retained while the computational cost is reduced compared to similar methods. Their relative performance is tested on some illustrative examples. |
| Keywords: | Geometric integrators linear differential equations initial value problems Lie groups |
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