Solving ODEs arising from non-selfadjoint Hamiltonian eigenproblems

@article{Jdar2000SolvingOA,
  title={Solving ODEs arising from non-selfadjoint Hamiltonian eigenproblems},
  author={Lucas J{\'o}dar and Marco Marletta},
  journal={Adv. Comput. Math.},
  year={2000},
  volume={13},
  pages={231-256}
}
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… CONTINUE READING
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