Solving Hamiltonian systems arising from ODE eigenproblems |
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Authors: | Carsten R. Maple Marco Marletta |
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Affiliation: | (1) Department of Computing, University of Luton, Park Square, Luton, LU1 3JU, UK;(2) Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, UK |
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Abstract: | This paper presents an algorithm for solving a linear Hamiltonian system arising in the study of certain ODE eigenproblems. The method follows the phase angles of an associated unitary matrix, which are essential for correct indexing of the eigenvalues of the ODE. Compared to the netlib code SL11F [11] the new method has the property that on many important problems – in particular, on matrix–vector Schrödinger equations – the cost of the integration is bounded independently of the eigenparameter λ. This allows large eigenvalues to be found much more efficiently. Numerical results show that our implementation of the new algorithm is substantially faster than the netlib code SL11F. |
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Keywords: | eigenvalue problem Hamiltonian system numerical integrator 34B 65L |
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