Hi Jeff
Sorry for the delay in replying. In your first problem, you haven't quite the boundary condition syntax correct. The following should work:
L = chebop(@(x,u) diff(u,4), [0,1]);
B = chebop(@(x,u) sin(x) + 0*u, [0,1]);
L.lbc = @(u) [diff(u,2), diff(u,3)];
L.rbc = @(u) [diff(u,2), diff(u,3)];
The y''''(x)=lambda*f(x)*y(x) problem should be possible also. Try something like the following, where sin is replaced by the m-file you wish to use to construct f:
f = chebfun(@sin, [0, 1]);
[V, D] = eigs(L, diag(f), 4);
Regards
Nick
P.S. Emailing discuss@chebfun.org or help@chebfun.org should result in speedier replies! :)

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08 Apr 2013

Chebfun V4
Numerical computation with functions instead of numbers.

Another question: I want to solve the eigenvalues and eigenfunctions of the following equation
y''''(x)=lambda*f(x)*y(x)
Here f(x) is a function defined in a seperate .m file. Is it possible to use chebfun to solve the eigenvalues and eigenfunctions?
Thanks.
Jeff

5

08 Apr 2013

Chebfun V4
Numerical computation with functions instead of numbers.

An excellent software!!! Definitely 5 star.
A quick question. I am using the chebfun function to find the eigenvalues and eigenfunctions of the following boundary value problem
D^4 y=lambda*y, y''(0)=y'''(0)=y''(1)=y'''(1)=0,
where D is the differential operator, lambda is the eigenvalue and the solution y is the corresponding eigenfunction.
I used the following code in chebfun:
L = chebop(@(x,u) diff(u,4), [0,1]);
L.lbc = @(u) diff(u,2);
L.lbc =@(u) diff(u,3);
L.rbc = @(u) diff(u,2);
L.rbc =@(u) diff(u,3);
[V,D] = eigs(L,trunc);
disp(diag(D)), toc
HOWEVER, the below error was reported
Error using eig
Matrix must be square.
Error in linop/eigs>bc_eig (line 288)
[V,D] = eig(full(Amat),full(Pmat));
Error in linop/eigs (line 94)
[V1,D1] = bc_eig(A,B,33,33,0,map,breaks);
Error in chebop/eigs (line 57)
[varargout{1:nargout}] = eigs(L,varargin{:});
Looks like I am on the right track but some nonsquare matrix caused that error. Sincerely appreciate your comments and suggestions.
Thanks.
Jeff

5

15 Feb 2013

Chebfun V4
Numerical computation with functions instead of numbers.

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