Can there be no examples in the patent application for invention method?

There must be an example.

If there are no examples, only the contents of the invention, then your technical scheme may not be fully disclosed, especially the process method and operation method. Without examples, those process parameters such as time, temperature and pressure will not be particularly limited or supported.

This invention needs substantial examination before it can be authorized. If there are no examples, it may be that the publicity is not enough, then the application will be rejected, just stating opinions, and there are no features that can support your technical scheme, because the modification cannot go beyond the scope recorded in your original application documents.