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

Liubov Efremova, Gerhard Freiling (2013)

Open Mathematics

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.

Numeric-analytical construction of Mathieu functions

Yu. A. Ryabov (1999)

Mathematica Bohemica

In this paper we present an iterative algorithm for the construction of Mathieu functions of any order N in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.

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