Paul B. Bailey, Anton Zettl
Abstract:
We study the relationship between the eigenvalues of separated self-adjoint
boundary conditions and coupled self-adjoint conditions. Given an arbitrary
real coupled boundary condition determined by a coupling matrix K we
construct a one parameter family of separated conditions and show that all
the eigenvalues for K and -K are extrema of the eigencurves of this family.
This characterization makes it possible to use the well known Prufer
transformation which has been used very successfully, both theoretically and
numerically, for separated conditions, also in the coupled case. In
particular, this characterization makes it possible to compute the
eigenvalues for any real coupled self-adjoint boundary condition using any
code which works for separated conditions.
Submitted June 4, 2012. Published July 23, 2012.
Math Subject Classifications: 05C38, 15A15, 05A15, 15A18
Key Words: Sturm-Liouville problems; computing eigenvalues;
separated and coupled boundary conditions.
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Paul B. Bailey 10950 N. La Canada Dr., #5107 Tucson, AZ 85737, USA email: paulbailey10950@comcast.net | |
Anton Zettl Department of Mathematical Sciences Northern Illinois University DeKalb, IL 60155, USA email: zettl@math.niu.edu |
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