Can we improve the quality of posts with tag differential-equations?

Question

This is an issue I've considered for a long time, and finally I decided to cry out loud here rather than think all by myself forever.

PDE-solving is the direct reason for my contact with Mathematica and this site, since then I always keep an eye on the questions tagged with differential-equations, and personally I feel the current situation unsatisfying: though being one of the most frequent tag in this site, it suffers a high unanswering rate, in fact, it's the highest in the top 10 of the frequent tag:

I believe the rate of low scoring posts under this tag is also high, but I haven't figure out a easy way to get the data.

I know solving differential equations is not easy, but is there nothing we can do to improve the current status?

Some possible ways in my mind:

1. Always suggest simplifying the problem as much as possible in the comment. This is valid for all the low quality question, but I think it's worth emphasizing here because guys struggling with differential equations are more likely to be newbies attracted by the seeming convenience of DSolve and NDSolve (according to my personal experience).

2. Always suggest adding background information of the equations in the comment. This may be embarrassing because we may still be unable to solve the problem even after knowing the origin of it, but anyway, it's better than nothing.

3. A collection or summarize for the known solution for some frequent issue, like the What are the most common pitfalls awaiting new users?, Why won't Parallelize speed up my code?, How to compile effectively?, etc.

4. Be more generous in upvoting answers under this tag. Indeed, many answers under this tag don't solve OP's question completely, but analyzing of differential equations is usually time consuming and frustrating: for me it's not rare to find nothing after hours of trial, and I believe I'm not the only one. Because of this, encouragement is necessary.

5. Kidnap some more DE experts here.

Are these feasible? Any other suggestions?

Answer 1

Although I am deeply interested in differential equations, especially in hyperbolic PDE's I don't find many interesting questions related. I believe there are several reasons and some of them were pointed out in the question.

• Most of beginners in Mathematica asking or answering questions find easily comprehensible problems e.g. in the plotting tag and this tag is definitely overestimated while differential-equations are surely underestimated, people don't want to take a bit of their time to understand actual problems therein. I guess it might be the most important reason.
• It seems that e.g. numerical solvers of differential equations are really advanced and powerful however we can find that symbolic solvers are unproportionally weaker. We know how many problems there are e.g. with Integrate (see e.g. Bug in Mathematica analytic integration?) and it is quite clear that similar issue (even stronger one) we find with DSolve. Symbolic differential equations are much more difficult than other problems ussually asked here. On the other hand e.g. Symbolics by M.Trott covered really interesting aspects of DE unfortunately we can find similar topics very rarely.
• I started using Mathematica when I attempted to solve symbolically certain very difficult nonlinear system of ODE's. Although I learnt much I couldn't succeed and left the problem unsolved (so far). My observation is that I've almost never exploited related techniques, this answer Working with a system of differential equations that cannot be solved explicitly is roughly related but symptomatically underestimated.

More activity on differential - equations here is definitely desired. Perhaps I will start soon asking a series of questions on PDE's however I'm not sure if this is reasonable since interesting questions on differential equations are rapidly covered with n-th time asked garbage on plotting.

Answer 2

Well, my background in PDEs is weak, although in ODEs it's a bit stronger. So it's a bit embarrassing to discover that I've given 55 answers - oops, now 56 - to differential equations questions. I've sought out the DE questions over the last year and a half primarily to learn better how to use NDSolve. I did this because I was preparing to teach a course in DE, mainly ODEs. Most(?) of my answers simply address coding issues (e.g, setting up the equations) and numerics issues. These are not usually very interesting, but if I found an answer, I like to help the OP.

The questions I am reluctant to answer:

• those that have half a page of parameter definitions
• those that have all subscripted variables (a personal horror, but understandably derived from the NDSolve docs)
• integro-differential equations (I'd have to figure them out, and I'd rather spend my time on other things)
• those that have have been answered in comments
• old questions of a user who has abandoned the site

It seems to me that a lot of the questions simply come from people's research, work, or homework - that is, of very localized interest. It's rare that there is something interesting related to the mathematics of the problem or to Mathematica. My experience has been that if the main interest in any question is in the mathematics, there probably aren't going to be very many upvotes, unless you can draw a pretty picture to go with it. :)

Well, looking back on what I've written, it seems to be more of an extended comment than a good answer. But I thought as one of the more active participants in the tag, I might contribute my views to the discussion.