Observation of thousands of type Ia supernovae should offer the most direct approach to probe the dark energy content of the universe. This will be undertaken by future large ground-based surveys followed by a space mission (SNAP/JDEM). We address the problem of extracting the cosmological parameters from the future data in a model independent approach, with minimal assumptions on the prior knowledge of some parameters. We concentrate on the comparison between a fiducial model and the fitting function and adress in particular the effect of neglecting (or not) the time evolution of the equation of state. We present a quantitative analysis of the bias which can be introduced by the fitting procedure. Such bias cannot be ignored as soon as the statistical errors from present data are drastically improved.
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