alright that works fine, thank you

ok then thats fine, can we also separate the negative roots aswell? like positive real, negative real, and imaginary all separate?

thanks

thanks that works fine

sorry, i didnt mean to say 'obtained' i meant to say 'introduced'. I think that the matrix 'eigen' is already the eigenmatrix, so we can find the eigenvalues straight from that. do i make sense?

the general solution will be of the form

<U(x),V(x),W(x)>= sum(i=1..4) (B[i].<u[i],v[i],w[i]>.exp(-k[i].x)      ,   where B[i] are constants.

so i need to determine <u[i],v[i],w[i]> and k[i] first.

I obtained k from non dimensionalising my wave problem. the determinant of 'eigen' is a characteristic equation for which we solve for eigenvalues,k. ultimately i will put a code to choose roots such that Re k[i]>0 or Re k[i]=0, Im k[i]>0 where we either want decay of the solution or to satisfy the radiation condition.

I formed 'eigen' from a system of DE's which i non dimensionalised. I understand that to find the general solution of a system of DE's we must find its eigenvalues and vectors etc, and this is what i am doing. i will then substitute these into the boundary conditions i have (which is the matrix 'BM') in order to find which frequencies, lambda, give det(BM) closest to zero.

Is my understanding here wrong?

Thank you for your time.

Hi Doug, I i think that i am now clear on my work.

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So basically, each root 'k' is also an eigenvalue. lambda is my frequency parameter. for each root 'k' there will be a corresponding eigenvector which we need to find. these eigenvectors are defined as <u[i],v[i],w[i]> . Thus for each lambda, we should end up with four eigenvalues 'k' and four eigenvectors '<u,v,w>' .  This information needs to then be substituted into the final matrix 'BM'.

I think that here we cannot ask maple to find eigenvectors. i think that we should manually ask maple to find the eigenvectors by letting one of the elements be 1. i have tried a bit but so far no luck.

if you could help that would be great,

thank you.

Sorry, i think that i have made a mistake in my logic. each 'k' is itself an eigenvalue, and as such has a corresponding eigenvector. the matrix 'eigen' is already an eigenmatrix. thus i shouldnt be asking maple to find the eigenvectors of that matrix as maple doesnt know that it is already an eigenmatrix. i need to think carefully about this and have another look at my code as i am also getting confused.

Thank you for spotting my flaw, i will have a look and come back to you.

and also, when i try

K := map( rhs@op, fsol );

this only displays all 'k' for one value of lambda.

thank you

yes i believe that you understand what i am trying to do.

the matrix 'eigen' is basically an eigen matrix. and the roots 'k' are its eigenvalues. therefore, we just need the corresponding eigenvectors, we are not interested in the eigenvalues that maple gives us.

now, u[1] to u[4] will be the first elements of each of the four eigenvectors, v[1] to v[4] will be the second element of the four eigenvectors and etc. I think that you understood this.

i do not want to remove lambda from the eigenmatrix because lambda is a frequency. i need this because i need to find the frequency at which the final matrix, M, has a determinant close to zero.

everything else i think that you have understood. so you see that my problem is to map the eigenvectors and k, onto the final matrix, M. the final matrix M is formed from the boundary conditions of the problem.

i hope that this is understandable, and that the question i am asking is not too much.

Thank you.

yah thats good thank you

and if its too complicated dont worry about it, thank you

Ok maybe i should just attach the file...

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It is a bit complicated, but i hope i explained everything clearly.

Please ask for any more explaination.

Thank you,

i think i should ask a different question, i will post it in the forum as it would be out of topic here

thank you for your help

ok i understand that, but i am trying to do a simple example first, because i actually have an equation that will give me eight solutions. i think perhaps that i didnt structure my question properly. i will re-do it and come back

thank you