Subject: use of constraints and initial values when solving DEs with power series. I have one problem of a DE where (only) the constraints are given alongside the DE (that I already particularly posted about regarding the convergence behaviour of it). And I have one problem where only the initial values are given (but no constraints). Now my theoretical question is: can I use them in a similar fashion (that is mechanically) to set up a power series, or is there a mechanical difference? And what happens mathematically in a mechanical way if both constraints and initial values are given?

Question

kainui · Answer

I would believe so, I can't see a reason as to why this wouldn't be the case. Whenever I solve a differential equation it's usually because it's modelling some thing. There are cases where solving something mathematically doesn't quite reflect what's going on in the real world, even to a reasonable approximation. For instance, the wave equation can be solved spherically and it implies the travelling of two kinds of waves, ones that travel outwards from a source and also waves that travel inwards from everywhere towards a single point. Of course this second scenario doesn't happen outside of a mathematical setting. To equations, they really don't know the difference between an initial or boundary condition, x's and t's are just variables that exist in a dimension that is indistinguishable on paper unless you're a person viewing it. I guess, if I understand you correctly, the question is if it matters? It can, but generally not. Everything is an approximation, so I guess it comes down to, does this method you're doing give a poor approximation or not? Do you have something in mind perhaps? I think you're probably likely to get a better answer from the people at http://math.stackexchange.com/ since they're generally at a much higher level than the people you'll find here. =)

anonymous · Answer

Well so far every of my questions have been answered :-) But I signed in and bookmarked it.