Explicit adaptive symplectic integrators for solving Hamiltonian systems |
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| Authors: | Sergio Blanes Arieh Iserles |
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| Institution: | 1. Instituto de Matem??tica Multidisciplinar, Universitat Polit??cnica de Valencia, 46022, Valencia, Spain
2. DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, Cambridge, CB3 0WA, UK
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| Abstract: | We consider Sundman and Poincaré transformations for the long-time numerical integration of Hamiltonian systems whose evolution occurs at different time scales. The transformed systems are numerically integrated using explicit symplectic methods. The schemes we consider are explicit symplectic methods with adaptive time steps and they generalise other methods from the literature, while exhibiting a high performance. The Sundman transformation can also be used on non-Hamiltonian systems while the Poincaré transformation can be used, in some cases, with more efficient symplectic integrators. The performance of both transformations with different symplectic methods is analysed on several numerical examples. |
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