Show problem ill-conditioned

I am attempting to show that

, with and is ill-conditioned.

I assumed a solution of the form which (of course) lead me to . Solutions to this equation are and .

Thus, . Now we use the boundary conditions given, leading to

.

How to go from here? The determinant of the coefficient matrix isn't particularly small, either.

Re: Show problem ill-conditioned

Quote:

Originally Posted by

**TheProphet** I am attempting to show that

, with

and

is ill-conditioned.

I assumed a solution of the form

which (of course) lead me to

. Solutions to this equation are

and

.

Thus,

. Now we use the boundary conditions given, leading to

.

How to go from here? The determinant of the coefficient matrix isn't particularly small, either.

The matrix of the coefficients is non singular, so that there is one and only one solution for and ... precisely is and ...

Kind regards

Re: Show problem ill-conditioned

Yes I know the matrix is nonsingular (I mentioned the determinant was non-zero). But I think the problem is to show that a small change in the data (i.e. boundary conditions) changes the solution by much. However, I don't find this to be the case.

Re: Show problem ill-conditioned

Re: Show problem ill-conditioned