Determination of leading coefficients in Sturm-Liouville operator from boundary measurements. II: Unicity and an engineering approach.
type: Item
instance of: scholarly article
title: Determination of leading coefficients in Sturm-Liouville operator from boundary measurements. II: Unicity and an engineering approach.
zbMATH Open document ID: 1033.65059
DOI: 10.1016/S0096-3003(00)00105-3
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: [ For part I see ibid. 125, 1--21 (2002; Zbl 1032.65078).] The authors present a scheme to determine the leading coefficient \(k(x)\) of the Sturm-Liouville operator \(Au(x) \equiv -(k(x)u'(x))'+q(x)u(x)\), \(x \in (a, b)\), with measured data given in the form of Dirichlet/Neumann type boundary conditions. The problem is reduced to a Cauchy problem for a first-order ordinary differential equation with respect to \(k(x)\). An analytical formula is presented for an approximate solution of the inverse problem. Numerical examples related to the accuracy of the solution and to essential features of the inverse problem are presented.
Mathematics Subject Classification ID: 65L09
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 1860978
zbMATH Keywords: boundary measurements
zbMATH Keywords: Sturm-Liouville operator
zbMATH Keywords: inverse problem
zbMATH Keywords: leading coefficient
zbMATH Keywords: Cauchy problem
zbMATH Keywords: numerical examples
author: Alemdar Hasanov
author: Zahir Muradoglu Seyidmamedov
MaRDI profile type: Publication
cites work: Solution of an inverse coefficient problem for an ordinary differential equation
cites work: Determination of leading coefficients in Sturm-Liouville operator from boundary measurements. I: A stripping algorithm
cites work: Q4125663
cites work: An Inverse Problem for the Steady State Diffusion Equation
cites work: On the determination of a differential equation from its spectral function
cites work: The inverse sturm‐liouville problem
cites work: An inverse problem for a Sturm-Liouville operator
Recommended article: Determination of leading coefficients in Sturm-Liouville operator from boundary measurements. I: A stripping algorithm
Recommended article: The determination of the leading coefficient in the monotone potential Sturm-Liouville operator from boundary measurements
Recommended article: Determination of the leading coefficient in fourth-order Sturm–Liouville operator from boundary measurements
Recommended article: An inverse polynomial method for the identification of the leading coefficient in the Sturm-Liouville operator from boundary measurements.
Recommended article: An inverse problem for computing a leading coefficient in the Sturm-Liouville operator by using the boundary data
Recommended article: Uniqueness Properties of The Solution of The Inverse Problem for The Sturm-Liouville Equation With Discontinuous Leading Coefficient
Recommended article: Determination of coefficients for a dissipative wave equation via boundary measurements
Recommended article: Uniqueness of recovery of the Sturm-Liouville operator with a spectral parameter quadratically entering the boundary condition
Recommended article: Q2950909
Recommended article: Error analysis of a multisingular inverse coefficient problem for the Sturm-Liouville operator based on boundary measurement.
description: scientific article; zbMATH DE number 1860978