- #1
AStaunton
- 105
- 1
just trying to solve PDEs by sep of variables;
am looking at laplace heat equation cylindrical problem and the equation that results is bessell function order 0...
in my notes, I have that the general solution to the equation is: R=AJ_0(r)+BY_0(r)
where J_0 and Y_0 apparently denote two independant functions to the equation and I think that both of these functions are 0 order...
My question is, how do J_0 and Y_0 differ from each other...looking on wikipedia page (my go to guide), it only shows a graph of one 0 order bessel, that is a max it 0 and has infinitely many roots..I think..
so for example if the function I just described corresponded to J_0 what would Y_0 look like...would it be pretty much the same but out of phase? I reasoned that this might be the case because this is how cos and sine are related...
Also advice on the key properties of bessell 0 order functions would be appreciated especially those properties that are relevant to finding eigenvalues in PDE sep variable problems...ie, At what values are the roots found and so on...
am looking at laplace heat equation cylindrical problem and the equation that results is bessell function order 0...
in my notes, I have that the general solution to the equation is: R=AJ_0(r)+BY_0(r)
where J_0 and Y_0 apparently denote two independant functions to the equation and I think that both of these functions are 0 order...
My question is, how do J_0 and Y_0 differ from each other...looking on wikipedia page (my go to guide), it only shows a graph of one 0 order bessel, that is a max it 0 and has infinitely many roots..I think..
so for example if the function I just described corresponded to J_0 what would Y_0 look like...would it be pretty much the same but out of phase? I reasoned that this might be the case because this is how cos and sine are related...
Also advice on the key properties of bessell 0 order functions would be appreciated especially those properties that are relevant to finding eigenvalues in PDE sep variable problems...ie, At what values are the roots found and so on...