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Inverse problems on star-type graphs: differential operators of different orders on different edges

100%

Yurko V.

Open Mathematics

2014

tom 12

nr 3

483-499

We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials

100%

Efremova L., Freiling G.

Open Mathematics

2013

tom 11

nr 11

2044-2051

We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.

Ograniczanie wyników

2 Open Mathematics

1 Efremova L.

1 Freiling G.

1 Yurko V.

1 2014

1 2013

Wyniki wyszukiwania

Inverse problems on star-type graphs: differential operators of different orders on different edges

Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials