gerbil Posted March 1, 2012 Share Posted March 1, 2012 Hello All, I have a question related to the fascinating topic of "Boundary Layer Theory". Take for example the simple equation mx'' + kx' + cx = 0 where k and c are finite constants and (m -> 0), (The derivative sign (') is by t) x(0) = 0 x'(0) = A > 0. In order to achieve a comprehension on what's going on near the point t = 0 when (m -> 0), it is suggested to take the change of variables t* = t/m. By that the former equation becomes, x'' + kx' + mcx = 0 (Now, the derivative sign (') is by t*). Now, moving into the limit or alternatively noticing that mcx is negligible, we can drop it and we get, x'' + kx' = 0 and now the solution is fairly easy. Books call this solution: "The inner solution" of the equation, since this solution describes the solution inside a boundary layer. My question is as follows: The idea of taking the change of variables t* = t/m, is just a mathematical trick or does it have a meaning (e.g. streching of the time scale, etc.)? If it has a meaning, i'd like to know its intuition. Best, Miki Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now