- #1
AStaunton
- 105
- 1
Just quick question about sep of variables..
say have function U(x,y)=X(x)Y(y)
when do separation of variables end up with some generic case that looks like:
X''/X=Y'/Y=lamda
my question is (and I think I know now the answer but would like confirmation), is what sign should the lamda be set to to make the problem easiest to solve...
And I think that it is down to which of the two, either X or Y that are going to give us the eigenvalues...
if X gives eigen values, then set lamda to the sign that allows the X differential equation easiest to solve and vise versa if Y ODE gives eigenvalues...
I'm just looking for a rule of thumb here or any tips anyone has..Thanks
say have function U(x,y)=X(x)Y(y)
when do separation of variables end up with some generic case that looks like:
X''/X=Y'/Y=lamda
my question is (and I think I know now the answer but would like confirmation), is what sign should the lamda be set to to make the problem easiest to solve...
And I think that it is down to which of the two, either X or Y that are going to give us the eigenvalues...
if X gives eigen values, then set lamda to the sign that allows the X differential equation easiest to solve and vise versa if Y ODE gives eigenvalues...
I'm just looking for a rule of thumb here or any tips anyone has..Thanks