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We present a numerical finite size scaling study of the localization lengthin long cylinders near the integer quantum Hall transition (IQHT) employing theChalker-Coddington network model. Corrections to scaling that decay slowly withincreasing system size make this analysis a very challenging numerical problem.In this work we develop a novel method of stability analysis that allows for abetter estimate of error bars. Applying the new method we find consistentresults when keeping second (or higher) order terms of the leading irrelevantscaling field. The knowledge of the associated (negative) irrelevant exponent$y$ is crucial for a precise determination of other critical exponents,including multifractal spectra of wave functions. We estimate $|y| > 0.4$,which is considerably larger than most recently reported values. Within thisapproach we obtain the localization length exponent $2.62 \pm 0.06$ confirmingrecent results. Our stability analysis has broad applicability to otherobservables at IQHT, as well as other critical points where corrections toscaling are present.

Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition