How can numerically compute eigenvalues of an ordinary differential equation in MATLAB?
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Lemuel Carlos Ramos Arzola
on 9 Feb 2019
Commented: Lemuel Carlos Ramos Arzola
on 15 Feb 2019
Hello,
I need to compute (numerically) the eigenvalues (L) of this singular ODE,
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/203422/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/203423/image.png)
Is it possible to use the Matlab function bvp4c? Or another?
Best regards,
Lemuel
2 Comments
Torsten
on 11 Feb 2019
https://math.stackexchange.com/questions/2507694/what-numerical-techniques-are-used-to-find-eigenfunctions-and-eigenvalues-of-a-d
Accepted Answer
Lemuel Carlos Ramos Arzola
on 13 Feb 2019
4 Comments
Torsten
on 14 Feb 2019
But as far as I see, you won't get an eigenvalue for an arbitrary choice of the third boundary condition.
E.g. if you have the ODE
y''+L*y = 0
y(0)=y(2*pi)=0,
the eigenvalues and eigenfunctions are L_n = (n/2)^2 and y_n(x) = sin(n*x/2) (n=1,2,3,...).
So if you choose y'(0)=1 as third boundary condition at x=0, e.g., every function y(x)=a*sin(sqrt(L)*x) with a*sqrt(L)=1 is a solution of the ODE, not only those for which a=2/n and L=(n/2)^2 (n=1,2,3.,,,).
More Answers (2)
Bjorn Gustavsson
on 11 Feb 2019
Have a look at what you can do with chebfun. It seem to cover eigenvalue/eigenfunctions of ODEs in some detail:
HTH
Torsten
on 11 Feb 2019
So you are left with the problem to find "a" such that
L_(0.25*(sqrt(a)-2)) (x) = 0 for x=sqrt(a).
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