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