Solving inverse Sturm-Liouville problems: theory and practice
نویسندگان
چکیده
منابع مشابه
A Least Squares Functional for Solving Inverse Sturm-Liouville Problems
Abstract. We present a variational algorithm for solving the classical inverse Sturm-Liouville problem in one dimension when two spectra are given. All critical points of the least squares functional are at global minima, which justifies minimization by a (conjugate) gradient descent algorithm. Numerical examples show that the resulting algorithm works quite reliable without tuning for particul...
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For any positive integer n and any given n distinct real numbers we construct a Sturm-Liouville problem whose spectrum is precisely the given set of n numbers. Such problems are of Atkinson type in the sense that the weight function or the reciprocal of the leading coefficient is identically zero on at least one subinterval.
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In the present paper, some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated. Uniqueness theorems for the solution of the inverse problem are proved, then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.
متن کاملNumerical solution of inverse Sturm–Liouville problems
A new algorithm is proposed for solving the inverse Sturm–Liouville problem of reconstructing a symmetric potential from eigenvalues. It uses Numerov’s method instead of the second order method of the related algorithm of Fabiano, Knobel and Lowe. An extension by Andrew and Paine of the asymptotic correction technique of Paine, de Hoog and Anderssen is the key to the success of the new algorith...
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ژورنال
عنوان ژورنال: ANZIAM Journal
سال: 2017
ISSN: 1445-8810
DOI: 10.21914/anziamj.v58i0.11739