The phrase
"analogous problems" means that two problems have similar concepts or elements, even if the specific details may vary. It suggests that solving one problem can help in finding a solution for the other problem because they are similar in some way.
Full definition
Each of these do have an enormous amount of precedent, which is largely largely binding (taqlid), but can be used
for analogous problems in new situations (qiyas).
The greatness and vaunted power and glory of the successive waves of empires that impinged on or conquered Israel (Egypt, Assyria, Babylon, Persia) posed
an analogous problem of idolatry in the human sphere.
Consider
the analogous problem of antibiotic resistance.
Forcing glacier ice over a resistant bed is
an analogous problem, at least to the extent that both the bird and the glacier — usually an ice sheet — have to balance force against resistance.