In numerical methods for ODE's, the model problem

y' = cy

where c is complex is regarded as sufficient in performing error analysis for different methods in solving ODE's.

Is it sufficient, and why? In my opinion, it overlooks many potential functions that can have different error forms.

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    $\begingroup$ Sufficient for what? This question is very unclear. Also, please give a reference for the claim "is regarded as..." $\endgroup$ – David Ketcheson Apr 22 '14 at 8:19