Abstract
We consider three numerical methods – one based on power series, one on the Magnus series and matrix exponentials, and one a library initial value code – for solving a linear system arising in non‐selfadjoint ODE eigenproblems. We show that in general, none of these methods has a cost or an accuracy which is uniform in the eigenparameter, but that for certain special types of problem, the Magnus method does yield eigenparameter‐uniform accuracy. This property of the Magnus method is explained by a trajectory‐shadowing result which, unfortunately, does not generalize to higher order Magnus type methods such as those in [11,12].
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Jódar, L., Marletta, M. Solving ODEs arising from non‐selfadjoint Hamiltonian eigenproblems. Advances in Computational Mathematics 13, 231–256 (2000). https://doi.org/10.1023/A:1018954227133
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DOI: https://doi.org/10.1023/A:1018954227133