I am in the pure math camp but was invited to referee an applied/interdisciplinary paper because I'm a specialist in the underlying mathematical tool. I want to ask for general guidance about evaluating an applied math paper compared to a pure math paper. For reference, the authors seem to be serious and well-published people, although only one is affiliated with a mathematics department.
About the paper itself: The main mathematical work comprises writing out a bunch of (fairly lengthy) equations that are meant to govern the process being modeled, then walking through a computational procedure (implemented outside the paper) to find approximate solutions, along with some supporting examples and figures. There are no theorems, proofs, or formal definitions, or really any serious attempt to justify the model, which has an "ad hoc" feel to it. The paper is loose on technicalities (e.g., minimal attention to the regularity of functions), yet at the same time uses lots of fancy jargon.
For these reasons, I'm not particularly enthusiastic about the paper, although I imagine it is par for an applied paper and I want to avoid any improper bias on my part. What are reasonable expectations and standards that I should apply?
Also: I am only asked to review the portions of the paper within my expertise. That said, I would hope to give some sort of opinion regarding the paper's merit.