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Improved High Order Integrators Based on the Magnus Expansion |
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| Authors: | S. Blanes F. Casas J. Ros |
| Affiliation: | (1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 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: | We build high order efficient numerical integration methods for solving the linear differential equation  = A(t)X based on the Magnus expansion. These methods preserve qualitative geometric properties of the exact solution and involve the use of single integrals and fewer commutators than previously published schemes. Sixth- and eighth-order numerical algorithms with automatic step size control are constructed explicitly. The analysis is carried out by using the theory of free Lie algebras. |
| Keywords: | Linear differential equations initial value problems numerical methods free Lie algebra Magnus expansion |
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