Talk:Boundary value problem

message: I can't get a mastery of the subject, but I wonder, is it possible that it bears on the problem of the 'joints' as mentioned by Socrates in the Symposium? That is, our senses allow us to perceive certain kinds of boundries intuitively but how do we decide where the joints lie otherwise. I know this is a very long shot 
( in the dark ) but perhaps someone will help me find a matchup somewhere in maths. wblakesx~~
:I'm not familiar with the passage, and don't have Plato handy, but it is conceivable that Socrates was fumbling towards a concept related in a crude way to the modern mathematical notion of 'boundary value problem'.  Such a connection would be fascinating, but if you find it, keep in mind this counts as original reseach, so Wikipedia is not the place to publish it. Brian Tvedt 12:50, 22 December 2005 (UTC)
thread_title:  as a non mathematician... 

message: There are many boundary value problems studied by mathematicians (mostly complex analysts and potential theorists) which do not fall under the heading of solutions of differential equations. For example, there is a lot of research into the boundary behaviour of (discontinuous) subharmonic functions, meromorphic functions, fine-continuous functions, etc. etc. I feel tempted (when I get some time) to write something about these problems somewhere, but the question is: do they belong here, or in a separate article, and if so, then what should it be titled? Madmath789 09:10, 1 August 2006 (UTC)
replies: text: I would suggest to start a section here and if it is too big create a separate article. Rex the first talk | contribs 23:00, 1 August 2006 (UTC)

text: Subharmonic functions solve an equation \Delta u = f with f<0, which satisfy certain maximum principles (see elliptic boundary value problem), this is still a PDE problem. Meromorphic functions satisfy the Cauchy-Riemann differential equation (a first order vector equation) so again, this is a PDE problem. Furthermore, the real part of a meromorphic function is harmonic, and the imaginary part is its "harmonic conjugate" (so again, see elliptic boundary value problem.) I don't know about fine continuous functions. Loisel 00:23, 18 April 2007 (UTC)
thread_title:  Other types of boundary value problems 

message: I have a couple of 2D Heat Equation and Laplace Equation PDE worked examples and graphs. One of which I put on the Heat equation page a while ago. Here Here is one and here Here is another. Feel free to use them on this page, if you think they might be appropriate. --Wtt 22:21, 17 April 2007 (UTC)
thread_title:  Diagrams 

message: I'm struggling (briefly) to consolidate the difference between boundary conditions in relation to boundary value problems and as the term is used in engineering. Where I've come to is that, while about the same thing, and while the physics dictating the equations used may involve BVPs, engineers tend to use the term much more generically - any set of inputs to some set of calculations are deemed to be the boundary conditions.
This may just be a local (mis)use of the term, and someone who has a better grasp on the concept from a mathematical background may be able to offer up a different POV. Just wondering if there's grounds for a short section on the other uses of the term, a Boundary Conditions (Engineering) page (though I don't see it growing beyond a stub,) or some other solution. Marimvibe (talk) 22:53, 20 June 2008 (UTC)
thread_title:  Boundary conditions outside of mathematics 

message: It could be helpful to discuss various special cases in subsections. As it stands, the article is sometimes unclear about how general the concept of a boundary value problem is. The graph at the top shows a closed boundary in two-dimensional space. But parts of the text seem to take boundary value problem to mean specifically two-point boundary value problem. 
In particular, there is a discussion of how initial value problems differ from boundary value problems, which states that the former only take conditions at t=0 as given, whereas the latter take as given conditions at t=0 and t=1. I think it should be made clear that this is just one example of a particular class of boundary value problems. Discussing two-point problems in detail, and then stating that there are many more general boundary value problems (like the one illustrated at the top of the page) would be helpful.
A distinction on this page between initial value problems and two-point boundary problems would be especially helpful for me as an editor of economics articles, because it's a crucial analytical difference in macroeconomics. Macroeconomic models based on adaptive expectations are generally initial value problems, because decision-makers' expectations in those models are determined by past experience, whereas macroeconomic models based on rational expectations are generally two-point boundary problems, because decision-makers' expectations in those models are determined by reasoning about the future. Also, from an economist's point of view, it would be helpful if this article mentioned that the distinction between initial value problems and two-point boundary value problems arises for difference equations as well as ordinary differential equations. In other words, it applies to dynamic systems in general, not to continuous-time dynamics only.
Any objections if I create a subsection specifically on two-point boundary problems? --Rinconsoleao (talk) 18:30, 2 March 2009 (UTC)
thread_title:  Special cases 

message: There are currently these examples provided in this article, presumably hinting on the heat equation:
:If the boundary gives a value to the normal derivative of the problem then it is a Neumann boundary condition. For example, if there is a heater at one end of an iron rod, then energy would be added at a constant rate but the actual temperature would not be known.
:If the boundary gives a value to the problem then it is a Dirichlet boundary condition. For example, if one end of an iron rod is held at absolute zero, then the value of the problem would be known at that point in space.
*In the Neumann example, what does the heat equation have to do with the normal derivative? What does a heater at one end of an iron rod have to do with a normal derivate?
*Conversely, what makes holding the rod at absolute zero different from placing a heater at this place, such that we don't work with the normal derivative?
Thanks, --Abdull (talk) 16:56, 15 February 2011 (UTC)
thread_title:  Normal derivative vs. temperature 

message: In Thomas H. Cormen's Introduction to Algorithms (3rd edition) p84, there's the following passage:
:We can use the substitution method to establish either upper or lower bounds on a recurrence. As an example, let us determine an upper bound on the recurrence T(n)=2T(n/2)+n:
:...
:Mathematical induction now requires us to show that our solution holds for the boundary conditions. Typically, we do so by showing that the boundary conditions are suitable as base cases for the inductive proof.
Does the definition of "boundary condition" as found on this article help me understand the use of "boundary condition" in this sentence? The article refers to it as a term in differential equations, which is not what Cormen's books deals with. --ToastieIL (talk) 16:11, 27 November 2011 (UTC)
thread_title:  Boundary condition in mathematical induction 

message: Why does the 'numerical solutions' section not mention finite difference methods? You should be able to choose between shooting method variations or finite difference methods to solve an arbitrary boundary value problem. Wiki47222 (talk) 00:42, 28 March 2019 (UTC)
thread_title:  Finite Difference Method in Numerical Section