Many times after the paper is published, the authors note that a major flaw has taken place in published work. . The flaw can either be in formulating the problem or in the methodology or assumptions or errors in measurement. The published results are totally wrong. In such cases, do authors on their own accept the mistake and withdraw the published paper?
In practice when an error in a published paper is found, the authors should write an erratum. In experimental research, when the paper is really important, the other researchers try to repeat experiments and when the expected results are impossible to find they conclude an error. This happened e.g. in so called "cold fusion" in the 80-ties. Finally, you should precise what you mean writing "witdraw the published paper". How it should be done in practice?
'Erratum' is generally written and published when the mistakes are minor and have no consequence to the final results or conclusions. If the mistake is major (escaped the attention of the reviewers), then the authors should bring this fact to the notice of the editor. The paper can be treated as officially withdrawn so that other researchers do not waste their time and effort in verifying the published results.
Ethics in research says that the authors should inform the editor either for making correction or to withdraw the paper if found erroneous elements in it. A good paper is followed by many researchers for doing their own research. If the error is not brought out to notice, it wastes the time of others who are consciously following it.
Another aspect can be like that it can be possible that some other researcher will notice your incorrect results and then it will be informed to the editor. In this situation, the reputation of the author and the institution to which he belongs is at the stake.
It should be brought to the notice of the editor, and the author should try correcting it.
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